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taco_7400 | deepcoder | You are given an array $a$ of length $n$ consisting of integers. You can apply the following operation, consisting of several steps, on the array $a$ zero or more times:
you select two different numbers in the array $a_i$ and $a_j$;
you remove $i$-th and $j$-th elements from the array.
For example, if $n=6$ and $a=[1, 6, 1, 1, 4, 4]$, then you can perform the following sequence of operations:
select $i=1, j=5$. The array $a$ becomes equal to $[6, 1, 1, 4]$;
select $i=1, j=2$. The array $a$ becomes equal to $[1, 4]$.
What can be the minimum size of the array after applying some sequence of operations to it?
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) is length of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
-----Output-----
For each test case, output the minimum possible size of the array after applying some sequence of operations to it.
-----Examples-----
Input
5
6
1 6 1 1 4 4
2
1 2
2
1 1
5
4 5 4 5 4
6
2 3 2 1 3 1
Output
0
0
2
1
0
-----Note-----
None | {"ground_truth": "{\"inputs\": [\"5\\n6\\n1 6 1 1 4 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 4\\n6\\n2 3 2 1 3 1\\n\", \"1\\n12\\n2 2 2 2 4 4 4 4 6 6 6 6\\n\", \"1\\n12\\n2 2 2 2 4 4 4 4 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 4 4 4 4 6 6 6 6\\n\", \"5\\n6\\n2 6 1 1 4 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 4\\n6\\n2 3 2 1 3 1\\n\", \"1\\n12\\n1 2 2 2 4 4 2 4 6 6 6 6\\n\", \"1\\n12\\n2 2 2 2 4 4 4 4 6 6 12 6\\n\", \"1\\n12\\n2 2 2 2 7 4 4 4 6 6 6 6\\n\", \"5\\n6\\n2 6 1 1 7 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 4\\n6\\n2 3 2 1 3 1\\n\", \"1\\n12\\n1 2 2 2 8 4 2 4 6 6 6 6\\n\", \"1\\n12\\n2 2 2 2 4 4 4 4 7 6 12 6\\n\", \"1\\n12\\n2 2 2 2 7 4 4 4 5 6 6 6\\n\", \"5\\n6\\n2 6 1 1 7 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 1\\n6\\n2 3 2 1 3 1\\n\", \"1\\n12\\n1 2 2 1 8 4 2 4 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 4 4 4 4 7 6 12 6\\n\", \"1\\n12\\n4 2 2 2 7 4 4 4 5 6 6 6\\n\", \"1\\n12\\n1 2 2 1 8 4 2 8 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 4 4 5 4 7 6 12 6\\n\", \"1\\n12\\n4 2 2 2 7 4 4 4 5 6 3 6\\n\", \"1\\n12\\n1 2 2 1 8 4 2 13 6 6 6 6\\n\", \"1\\n12\\n1 2 2 1 10 4 2 13 6 6 6 6\\n\", \"1\\n12\\n2 2 2 1 10 4 2 13 6 6 6 6\\n\", \"1\\n12\\n2 2 2 1 10 4 2 13 6 6 6 1\\n\", \"1\\n12\\n2 2 2 1 10 4 2 21 6 6 6 1\\n\", \"1\\n12\\n2 2 2 2 10 4 2 21 6 6 6 1\\n\", \"1\\n12\\n2 2 2 2 10 4 2 21 8 6 6 1\\n\", \"1\\n12\\n2 2 2 2 10 4 2 21 8 8 6 1\\n\", \"1\\n12\\n2 2 2 2 10 4 1 21 8 8 6 1\\n\", \"1\\n12\\n2 2 2 2 10 7 1 21 8 8 6 1\\n\", \"1\\n12\\n2 2 2 2 10 7 1 33 8 8 6 1\\n\", \"1\\n12\\n2 2 2 2 10 7 1 1 8 8 6 1\\n\", \"1\\n12\\n1 2 2 2 4 4 4 4 6 6 6 2\\n\", \"5\\n6\\n2 6 1 1 4 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 2 4 5 4\\n6\\n2 3 2 1 3 1\\n\", \"1\\n12\\n2 2 2 2 4 4 4 4 11 6 12 6\\n\", \"1\\n12\\n2 2 2 2 7 4 4 7 6 6 6 6\\n\", \"5\\n6\\n2 6 1 1 7 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 4\\n6\\n3 3 2 1 3 1\\n\", \"1\\n12\\n1 2 2 2 8 4 4 4 6 6 6 6\\n\", \"1\\n12\\n2 1 2 2 4 4 4 4 7 6 12 6\\n\", \"1\\n12\\n2 2 2 2 7 6 4 4 5 6 6 6\\n\", \"1\\n12\\n1 2 2 3 4 4 5 4 7 6 12 6\\n\", \"1\\n12\\n4 2 2 2 7 3 4 4 5 6 3 6\\n\", \"1\\n12\\n1 2 2 1 8 6 2 13 6 6 6 6\\n\", \"1\\n12\\n1 2 2 1 10 4 1 13 6 6 6 6\\n\", \"1\\n12\\n2 2 2 2 10 4 2 13 6 6 6 6\\n\", \"1\\n12\\n2 2 2 1 10 4 2 21 6 9 6 1\\n\", \"1\\n12\\n2 4 2 2 10 4 2 21 6 6 6 1\\n\", \"1\\n12\\n2 1 2 2 10 4 2 21 8 6 6 1\\n\", \"1\\n12\\n2 2 2 2 10 9 1 21 8 8 6 1\\n\", \"1\\n12\\n2 2 2 2 10 7 1 33 8 8 6 2\\n\", \"1\\n12\\n2 2 2 2 10 6 1 1 8 8 6 1\\n\", \"1\\n12\\n1 2 2 1 4 4 4 4 6 6 6 2\\n\", \"5\\n6\\n2 6 1 1 4 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 2 4 5 4\\n6\\n2 3 2 1 2 1\\n\", \"1\\n12\\n2 2 2 2 4 1 4 4 11 6 12 6\\n\", \"1\\n12\\n2 2 3 2 7 4 4 7 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 9 4 4 4 6 6 6 6\\n\", \"1\\n12\\n2 1 2 2 4 4 4 4 7 6 21 6\\n\", \"1\\n12\\n2 2 2 2 7 6 4 4 5 2 6 6\\n\", \"1\\n12\\n1 2 2 3 4 4 5 1 7 6 12 6\\n\", \"1\\n12\\n4 2 2 2 10 3 4 4 5 6 3 6\\n\", \"1\\n12\\n1 2 2 1 8 6 2 13 12 6 6 6\\n\", \"1\\n12\\n1 2 2 1 19 4 1 13 6 6 6 6\\n\", \"1\\n12\\n2 2 2 2 18 4 2 13 6 6 6 6\\n\", \"1\\n12\\n2 1 2 2 10 4 3 21 8 6 6 1\\n\", \"1\\n12\\n2 2 2 2 10 9 1 21 8 8 10 1\\n\", \"1\\n12\\n3 2 2 2 10 7 1 33 8 8 6 2\\n\", \"1\\n12\\n2 2 2 2 10 6 1 1 7 8 6 1\\n\", \"1\\n12\\n2 2 2 1 4 1 4 4 11 6 12 6\\n\", \"1\\n12\\n2 2 3 2 7 4 4 11 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 9 4 4 4 6 4 6 6\\n\", \"1\\n12\\n2 1 1 2 4 4 4 4 7 6 21 6\\n\", \"1\\n12\\n2 2 2 2 7 6 4 4 1 2 6 6\\n\", \"1\\n12\\n1 2 2 3 4 5 5 1 7 6 12 6\\n\", \"1\\n12\\n4 2 2 2 10 3 4 4 5 7 3 6\\n\", \"1\\n12\\n1 2 2 1 8 7 2 13 12 6 6 6\\n\", \"1\\n12\\n1 2 2 1 19 4 1 13 6 6 6 11\\n\", \"1\\n12\\n2 2 2 2 18 4 2 17 6 6 6 6\\n\", \"1\\n12\\n2 1 2 2 10 4 3 21 8 6 4 1\\n\", \"1\\n12\\n1 2 2 2 10 9 1 21 8 8 10 1\\n\", \"1\\n12\\n3 2 2 2 10 7 1 33 8 8 3 2\\n\", \"1\\n12\\n2 2 2 2 9 6 1 1 7 8 6 1\\n\", \"1\\n12\\n2 3 2 1 4 1 4 4 11 6 12 6\\n\", \"1\\n12\\n1 2 4 2 9 4 4 4 6 4 6 6\\n\", \"1\\n12\\n2 1 1 2 4 4 4 4 7 6 28 6\\n\", \"1\\n12\\n2 2 2 3 7 6 4 4 1 2 6 6\\n\", \"1\\n12\\n1 2 2 3 4 2 5 1 7 6 12 6\\n\", \"1\\n12\\n1 2 2 1 19 4 1 13 11 6 6 11\\n\", \"1\\n12\\n2 2 2 2 18 3 2 17 6 6 6 6\\n\", \"1\\n12\\n1 2 2 2 10 11 1 21 8 8 10 1\\n\", \"1\\n12\\n2 2 2 2 14 6 1 1 7 8 6 1\\n\", \"1\\n12\\n2 3 2 1 4 1 4 4 11 8 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 4 4 7 6 28 6\\n\", \"1\\n12\\n2 2 1 3 7 6 4 4 1 2 6 6\\n\", \"1\\n12\\n1 2 2 3 4 2 5 1 3 6 12 6\\n\", \"1\\n12\\n1 2 2 1 19 4 1 13 11 6 6 13\\n\", \"1\\n12\\n2 2 3 2 18 3 2 17 6 6 6 6\\n\", \"1\\n12\\n1 2 1 2 10 11 1 21 8 8 10 1\\n\", \"1\\n12\\n2 2 4 2 14 6 1 1 7 8 6 1\\n\", \"1\\n12\\n2 2 2 1 4 1 4 4 11 8 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 4 4 7 6 44 6\\n\", \"1\\n12\\n2 2 1 3 7 6 4 8 1 2 6 6\\n\", \"1\\n12\\n1 2 2 3 2 2 5 1 3 6 12 6\\n\", \"1\\n12\\n1 2 1 1 19 4 1 13 11 6 6 13\\n\", \"1\\n12\\n2 2 3 2 18 2 2 17 6 6 6 6\\n\", \"1\\n12\\n1 2 1 2 10 11 1 21 3 8 10 1\\n\", \"1\\n12\\n2 2 2 1 4 1 1 4 11 8 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 4 4 2 6 44 6\\n\", \"1\\n12\\n2 2 1 3 7 6 4 8 2 2 6 6\\n\", \"1\\n12\\n1 2 4 3 2 2 5 1 3 6 12 6\\n\", \"1\\n12\\n1 2 1 2 10 11 1 21 3 1 10 1\\n\", \"1\\n12\\n2 1 1 4 4 4 4 4 2 6 44 10\\n\", \"1\\n12\\n2 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\"1\\n12\\n1 2 2 2 10 4 1 21 8 8 10 1\\n\", \"1\\n12\\n2 2 2 2 7 6 1 1 7 8 6 1\\n\", \"1\\n12\\n2 3 2 1 4 1 1 4 11 8 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 7 4 7 6 28 6\\n\", \"1\\n12\\n1 2 2 3 4 2 5 1 3 6 13 6\\n\", \"1\\n12\\n4 2 3 2 18 3 2 17 6 6 6 6\\n\", \"1\\n12\\n2 2 2 1 4 1 4 4 11 13 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 4 7 7 6 44 6\\n\", \"1\\n12\\n1 2 1 1 19 4 1 13 11 7 6 13\\n\", \"1\\n12\\n2 2 3 2 10 2 2 17 6 6 6 6\\n\", \"1\\n12\\n2 1 1 7 4 4 4 4 2 6 44 6\\n\", \"1\\n12\\n1 2 2 3 2 2 5 1 3 10 12 6\\n\", \"1\\n12\\n2 1 1 4 4 4 4 4 2 5 44 10\\n\", \"1\\n12\\n2 2 1 2 10 16 1 21 3 1 10 1\\n\", \"1\\n12\\n2 1 1 4 4 4 4 2 3 6 44 10\\n\", \"1\\n12\\n1 2 1 3 7 6 4 11 2 2 6 2\\n\", \"1\\n12\\n1 1 4 3 2 2 5 1 3 6 11 2\\n\", \"5\\n6\\n1 6 1 1 4 4\\n2\\n1 2\\n2\\n1 1\\n5\\n4 5 4 5 4\\n6\\n2 3 2 1 3 1\\n\"], \"outputs\": [\"0\\n0\\n2\\n1\\n0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n0\\n2\\n1\\n0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n0\\n2\\n1\\n0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", 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taco_7401 | deepcoder | You are given n patterns p_1, p_2, ..., p_n and m strings s_1, s_2, ..., s_m. Each pattern p_i consists of k characters that are either lowercase Latin letters or wildcard characters (denoted by underscores). All patterns are pairwise distinct. Each string s_j consists of k lowercase Latin letters.
A string a matches a pattern b if for each i from 1 to k either b_i is a wildcard character or b_i=a_i.
You are asked to rearrange the patterns in such a way that the first pattern the j-th string matches is p[mt_j]. You are allowed to leave the order of the patterns unchanged.
Can you perform such a rearrangement? If you can, then print any valid order.
Input
The first line contains three integers n, m and k (1 ≤ n, m ≤ 10^5, 1 ≤ k ≤ 4) — the number of patterns, the number of strings and the length of each pattern and string.
Each of the next n lines contains a pattern — k characters that are either lowercase Latin letters or underscores. All patterns are pairwise distinct.
Each of the next m lines contains a string — k lowercase Latin letters, and an integer mt (1 ≤ mt ≤ n) — the index of the first pattern the corresponding string should match.
Output
Print "NO" if there is no way to rearrange the patterns in such a way that the first pattern that the j-th string matches is p[mt_j].
Otherwise, print "YES" in the first line. The second line should contain n distinct integers from 1 to n — the order of the patterns. If there are multiple answers, print any of them.
Examples
Input
5 3 4
_b_d
__b_
aaaa
ab__
_bcd
abcd 4
abba 2
dbcd 5
Output
YES
3 2 4 5 1
Input
1 1 3
__c
cba 1
Output
NO
Input
2 2 2
a_
_b
ab 1
ab 2
Output
NO
Note
The order of patterns after the rearrangement in the first example is the following:
* aaaa
* __b_
* ab__
* _bcd
* _b_d
Thus, the first string matches patterns ab__, _bcd, _b_d in that order, the first of them is ab__, that is indeed p[4]. The second string matches __b_ and ab__, the first of them is __b_, that is p[2]. The last string matches _bcd and _b_d, the first of them is _bcd, that is p[5].
The answer to that test is not unique, other valid orders also exist.
In the second example cba doesn't match __c, thus, no valid order exists.
In the third example the order (a_, _b) makes both strings match pattern 1 first and the order (_b, a_) makes both strings match pattern 2 first. Thus, there is no order that produces the result 1 and 2. | {"ground_truth": "{\"inputs\": [\"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\ncbb 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"5 10 1\\n_\\nb\\nc\\nd\\na\\nc 2\\na 5\\nb 5\\nb 2\\nd 5\\na 3\\nd 5\\nc 2\\nb 2\\nd 2\\n\", \"5 5 3\\ncaa\\nabb\\ncbb\\naac\\ncbc\\ncbc 5\\naac 4\\nabb 2\\ncbb 3\\ncaa 1\\n\", \"4 10 1\\n_\\nb\\nc\\na\\nc 1\\na 4\\nb 2\\na 4\\nb 3\\nb 1\\nb 3\\na 3\\nb 1\\nc 1\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bcd\\nabcd 3\\nabba 2\\ndbcd 5\\n\", \"2 1 1\\ns\\nb\\nb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbc\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 4\\n_a_c\\n_aac\\nb__a\\n__cb\\nab__\\n__ab\\n_c__\\n____\\n_bbd\\nb_bc\\nbcbc 8\\nabac 8\\ncadc 8\\ncaac 8\\ndaab 8\\naccb 8\\ncbcd 8\\nabbd 8\\nbdba 8\\nbcac 8\\n\", \"2 1 4\\naaaa\\naaab\\naaaa 2\\n\", \"10 10 3\\nbbb\\nbd_\\n_bc\\nb_c\\ndba\\ndad\\n_aa\\nad_\\nacc\\n_ca\\nabd 4\\ncdd 9\\nccc 8\\nbbc 6\\nbab 1\\ndda 6\\ncca 1\\ndca 4\\ncac 5\\nbdb 10\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\ncaa 10\\naab 7\\n\", \"10 10 2\\ncd\\ndd\\nab\\naa\\nac\\nc_\\nba\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 1\\nac 9\\nac 4\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"10 10 4\\n_a_c\\n_aac\\nb__a\\n__cb\\nab__\\n__ab\\n_c__\\n____\\n_bbd\\nb_bc\\nbcbc 8\\nabac 8\\ncadc 8\\ncaac 8\\ndaab 8\\naccb 8\\ncbcd 8\\nabbd 8\\nbdba 8\\nbcad 8\\n\", \"2 2 2\\na_\\n_b\\nab 2\\nab 2\\n\", \"5 0 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bdc\\nabcd 4\\nabba 2\\ndbcd 5\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\ndab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\ncaa 10\\naab 7\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\ndcb_\\nabcd 1\\nabba 2\\ndcbd 5\\n\", \"10 0 3\\ncaa\\nd_c\\nba_\\naba\\nbba\\n_bc\\n_ba\\nbab\\nbcc\\n_aa\\nabb 0\\ncca 8\\nacc 0\\ncbc 4\\naca 6\\nbab 5\\naca 2\\ncab 8\\naaa 2\\ndcb 1\\n\", \"5 2 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bcd\\nabcd 4\\nabba 2\\ndbcd 4\\n\", \"2 1 1\\ns\\na\\nb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"10 10 2\\ncd\\ndd\\nab\\naa\\nac\\nc_\\nba\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 1\\nac 10\\nac 4\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bdc\\nabcd 4\\nabba 2\\ndbcd 5\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\na__\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bdc\\naccd 4\\nabba 2\\ndbcd 5\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nac 6\\nba 4\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nac 6\\nba 8\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 4\\ncbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\ncaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 2\\nacb 0\\ncbc 2\\ncaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\ncbb 2\\nbaa 10\\nbca 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"5 10 1\\n_\\nb\\nc\\nd\\na\\nc 2\\na 5\\nb 5\\nb 2\\nd 5\\na 3\\nd 5\\nc 2\\na 2\\nd 2\\n\", \"5 5 3\\ncaa\\nabb\\ncbb\\naac\\ncbc\\ncbc 5\\ncaa 4\\nabb 2\\ncbb 3\\ncaa 1\\n\", \"4 10 1\\n_\\nb\\nc\\na\\nc 1\\na 4\\nb 2\\na 4\\nb 3\\nb 1\\na 3\\na 3\\nb 1\\nc 1\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\ndcb_\\nabcd 3\\nabba 2\\ndbcd 5\\n\", \"2 1 1\\ns\\nb\\nc 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbc\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncc 9\\ncb 4\\naa 1\\naa 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbbb\\nbd_\\n_bc\\nb_c\\ndba\\ndad\\n_aa\\nad_\\nacc\\n_ca\\nabd 4\\ncdd 9\\nccc 8\\nbbc 6\\nbab 1\\ndda 6\\nccb 1\\ndca 4\\ncac 5\\nbdb 10\\n\", \"10 10 2\\ndc\\ndd\\nab\\naa\\nac\\nc_\\nba\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 1\\nac 9\\nac 4\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nac__\\n_bcd\\nabcd 4\\nabba 2\\ndbcd 5\\n\", \"1 1 3\\n__d\\ncba 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacc 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"2 1 1\\ns\\na\\nb 2\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncb 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 6\\nbab 7\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"10 10 2\\ncd\\ndd\\nab\\naa\\nac\\nc_\\nab\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 1\\nac 10\\nac 4\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\ncd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 3 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\na__\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"5 3 4\\nd_b_\\n__b_\\naaaa\\nab__\\n_bdc\\naccd 4\\nabba 2\\ndbcd 5\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nbcc 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 2\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 1\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nac 6\\nba 4\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nbbb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nbc 6\\nba 8\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbaa 10\\nbba 8\\nbcb 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nbcc\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 3 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\ncaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\ncbb 2\\nbaa 10\\nbac 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"5 2 3\\ncaa\\nabb\\ncbb\\naac\\ncbc\\ncbc 5\\ncaa 4\\nabb 2\\ncbb 3\\ncaa 1\\n\", \"4 10 1\\n_\\nb\\nc\\na\\nc 1\\na 4\\nb 2\\na 4\\nb 3\\nb 1\\na 3\\na 4\\nb 1\\nc 1\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\ndcb_\\nabcd 3\\nabba 2\\ndcbd 5\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\n_b\\nbc\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncc 9\\ncb 4\\naa 1\\naa 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbbb\\nbd_\\n_bc\\nb_c\\ndba\\ndad\\n_aa\\nad_\\nacc\\n_ca\\nabd 2\\ncdd 9\\nccc 8\\nbbc 6\\nbab 1\\ndda 6\\nccb 1\\ndca 4\\ncac 5\\nbdb 10\\n\", \"10 10 2\\ndc\\ndd\\nab\\naa\\nac\\nc_\\nba\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 0\\nac 9\\nac 4\\n\", \"2 0 2\\na_\\n_b\\nab 2\\nab 2\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacc 4\\nbbc 2\\nbaa 10\\nbba 8\\nbac 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 0\\ncb 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 6\\nbab 7\\nbbb 7\\nbaa 10\\naad 10\\naab 7\\n\", \"10 10 2\\ncd\\ndd\\nab\\naa\\nac\\nc_\\nab\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nbc 1\\naa 10\\nca 2\\nbc 1\\nac 1\\nac 10\\nac 4\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\n_c\\nca\\nb_\\ncd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 3 3\\nbb_\\nabc\\nbac\\nbaa\\n_ab\\n_b_\\n___\\nb__\\n_a_\\na__\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 7\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nadb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nbcc 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 1\\ncb 3\\ncc 9\\ndb 4\\naa 1\\nac 6\\nba 4\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nbbb 1\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 5\\naaa 2\\nccb 1\\n\", \"10 10 2\\na_\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nbc 6\\nba 8\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbab 10\\nbba 8\\nbcb 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nbcc\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\nbaa 6\\nbba 8\\nbca 1\\ncac 8\\naaa 2\\nccb 1\\n\", \"10 3 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_bc\\n_ba\\nbac\\nccb\\n_aa\\nabb 1\\ncca 8\\nacb 0\\ncbc 2\\ncaa 6\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\ndcb 1\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nbba\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacb 4\\ncbb 2\\nbaa 10\\nbac 8\\nbca 1\\ncab 8\\naaa 2\\nccb 6\\n\", \"4 8 1\\n_\\nb\\nc\\na\\nc 1\\na 4\\nb 2\\na 4\\nb 3\\nb 1\\na 3\\na 4\\nb 1\\nc 1\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\ndcb_\\ndcba 3\\nabba 2\\ndcbd 5\\n\", \"10 6 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\n_b\\nbc\\n__\\naa\\ncc 6\\naa 10\\naa 6\\nbb 3\\ncc 9\\ncb 4\\naa 1\\naa 6\\nba 4\\nbc 3\\n\", \"10 10 3\\nbbb\\nbd_\\n_bc\\nb_c\\ndba\\ndad\\n_aa\\nad_\\nacc\\n_ba\\nabd 2\\ncdd 9\\nccc 8\\nbbc 6\\nbab 1\\ndda 6\\nccb 1\\ndca 4\\ncac 5\\nbdb 10\\n\", \"10 10 2\\ndc\\ndd\\nab\\naa\\nac\\nc_\\nba\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nac 1\\naa 10\\nca 2\\nbc 1\\nac 0\\nad 9\\nac 4\\n\", \"2 0 2\\na_\\n_b\\nab 2\\nac 2\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_cc\\n_ba\\nbac\\nccb\\n_ab\\nabb 1\\ncca 8\\nacc 4\\nbbc 2\\nbaa 10\\nbba 8\\nbac 1\\nbac 8\\naaa 2\\nccb 6\\n\", \"10 10 3\\nbb_\\nabc\\nbac\\nbab\\n_ab\\n_b_\\n___\\nb__\\n_a_\\n__a\\nbac 7\\ncaa 10\\nbac 7\\naba 10\\nabc 6\\nbab 7\\nbbb 7\\nbaa 10\\naad 10\\naab 7\\n\", \"10 10 2\\ncd\\ndd\\nab\\naa\\nac\\nc_\\nab\\nca\\ndc\\n__\\nda 8\\nda 4\\ndd 4\\nbc 1\\naa 10\\nca 2\\nbc 2\\nac 1\\nac 10\\nac 4\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\n_c\\nca\\nb_\\ncd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 6\\n\", \"10 3 3\\nbb_\\nabc\\nbac\\nbaa\\n_ab\\n_b_\\n___\\nb__\\n_a_\\na__\\ncab 7\\ncaa 10\\nbac 7\\naba 10\\nabc 7\\nbab 2\\nbbb 7\\nbaa 10\\naac 10\\naab 7\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 1\\ncb 3\\ncc 9\\ndb 4\\naa 1\\nac 6\\nba 4\\nbc 0\\n\", \"10 10 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4\\nabba 2\\ndbcd 5\\n\", \"10 10 2\\n_a\\na_\\nab\\nbb\\nc_\\nca\\nb_\\ncd\\n__\\naa\\ncc 6\\naa 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nab 6\\nba 4\\nbc 3\\n\", \"10 10 3\\ncaa\\nc_c\\nba_\\naca\\nabb\\n_bc\\n_ba\\ncab\\nccb\\n_aa\\nabb 2\\ncca 8\\nacb 4\\nbbc 2\\nbaa 10\\nbba 8\\nbca 1\\ncab 8\\naaa 2\\nccb 1\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\nb_\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 1\\ncb 3\\ncc 8\\ncb 4\\naa 1\\nac 6\\nba 4\\nbc 3\\n\", \"10 10 2\\n_a\\na_\\nba\\nbb\\nc_\\nca\\n_b\\nbd\\n__\\naa\\ncc 6\\nab 10\\naa 6\\ncb 3\\ncc 9\\ncb 4\\naa 1\\nbc 6\\nba 8\\nbc 3\\n\", \"5 3 4\\n_b_d\\n__b_\\naaaa\\nab__\\n_bcd\\nabcd 4\\nabba 2\\ndbcd 5\\n\", \"2 2 2\\na_\\n_b\\nab 1\\nab 2\\n\", \"1 1 3\\n__c\\ncba 1\\n\"], \"outputs\": [\"NO\\n\", \"NO\\n\", \"YES\\n5 4 3 2 1 \\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n8 9 10 7 6 5 4 3 2 1 \\n\", \"NO\\n\", \"NO\\n\", \"YES\\n10 7 8 9 6 5 4 3 2 1 \\n\", \"NO\\n\", \"NO\\n\", \"YES\\n8 9 10 7 6 5 4 3 2 1\\n\", 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\"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n2 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n2 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n2 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n2 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n2 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", 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taco_7402 | deepcoder | You are given a set of points on a straight line. Each point has a color assigned to it. For point a, its neighbors are the points which don't have any other points between them and a. Each point has at most two neighbors - one from the left and one from the right.
You perform a sequence of operations on this set of points. In one operation, you delete all points which have a neighbor point of a different color than the point itself. Points are deleted simultaneously, i.e. first you decide which points have to be deleted and then delete them. After that you can perform the next operation etc. If an operation would not delete any points, you can't perform it.
How many operations will you need to perform until the next operation does not have any points to delete?
-----Input-----
Input contains a single string of lowercase English letters 'a'-'z'. The letters give the points' colors in the order in which they are arranged on the line: the first letter gives the color of the leftmost point, the second gives the color of the second point from the left etc.
The number of the points is between 1 and 10^6.
-----Output-----
Output one line containing an integer - the number of operations which can be performed on the given set of points until there are no more points to delete.
-----Examples-----
Input
aabb
Output
2
Input
aabcaa
Output
1
-----Note-----
In the first test case, the first operation will delete two middle points and leave points "ab", which will be deleted with the second operation. There will be no points left to apply the third operation to.
In the second test case, the first operation will delete the four points in the middle, leaving points "aa". None of them have neighbors of other colors, so the second operation can't be applied. | {"ground_truth": "{\"inputs\": [\"aabb\\n\", \"aabcaa\\n\", \"abbcccbba\\n\", \"aaaaaaaaaaa\\n\", \"aaaaaaaaabbbbbaaaabaaaaaaaaaaaaaaaaabaaaaaabbbbbbbaaabbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaa\\n\", \"abc\\n\", \"a\\n\", \"ab\\n\", \"ba\\n\", \"aaabbb\\n\", \"abababababab\\n\", \"aaabbbbbbaaa\\n\", \"bbbbbbbbbbbbbbbbbbbbbbddddddddddddddddaaaaaaaaaaaaaccccccccbbbbbbbaaaaaaaaaabbbbbbbbaaaaaaaaaacccccc\\n\", \"bbeeeeaaaaccccbbbbeeeeeeeeeeaaaaddddddddddddddddddbbbbbbbdddeeeeeeeeeeaaaaaaaaeeeeeaaaaadbbbbbbbeadd\\n\", \"abaabaaaabaabbaabaabaabbaabbaabaaaabbaabbaabaabaabaabbabaabbababbababbabaababbaaabbbbaabbabbaabbaaba\\n\", \"bbbbbbbbbbbbbbbbbbbbbbbbbbddddddddddddddddddddddddddddddddddddddcccccccccccccccccccccccccccccccccccc\\n\", \"bcddbbdaebbaeaceaaebaacacbeecdbaeccaccbddedaceeeeecccabcabcbddbadaebcecdeaddcccacaeacddadbbeabeecadc\\n\", 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\"bbbbbbbcaaaaaaaaaaaccccccaaaaaaaaaaaaaaccccccccaaaaaaaaabbbbbbccbbbaaaaaabccccccaaaacaaacccccccccccb\\n\", \"ccccccccccccccccccccccccccccccdcaaaaaaaaaaaaaaccccccccccccccccccdccccccccccccccccccccccccccccccccccc\\n\", \"bbbbbbaaaaaabbbbbbbbbbbbbbbbbbbbbbbbaaaaabbbbbbbbbbbbaabbbbbbbacbbbbaaabbbbbbbaaabbbbaaaaabbbbbaaaaa\\n\", \"bddbeddebbeaccdeeeceaebbdaabecbcaeaaddbbeadebbbbebaddcdcdecaeebaceaeeabbbccccaaebbadcaaaebcedccecced\\n\", \"cbbcacacccaaabcddddbcbadcbadaadadcddccdcabdcbcddcbcaccdccbdbdcadabccabcacccdcbbabbbddccccacacdcabcbd\\n\", \"abaabbaabbabbabbbbbaaabbabaababbababbaaabbaababbaabaabaabaabbaabbaaaabaabbaabbaabaabaabbaabaaaabaaba\\n\", \"aaccaaccaaaaccaaabbbcbaccbacabcabbccbccbacbcbbcbaacccbaaaccaacbbbaccacccabbacccacacbacaabacbacccbccc\\n\", \"aaabbbbbbaaabbbbaaabbbbbbaaaaaaaaaaababbbaaaaaaaaabbbbbbbbaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\n\", \"_\\n\", \"ccccccaaaaaaaaaabbbbbbbbaaaaaaaaaabbbbbbbccccccccaadaaaaaaaaaaddddddddddddddadbbbbbbbbbbbbbbbbbbbbbb\\n\", \"cccccccccccccccccccccccccccaaaaaccccaaabbbbbbbbbbbbbbbbbbbbbbbbcbbbbbbbbbabbbbbbbabaaaaabbbbbbbbbaaa\\n\", \"baabaa\\n\", \"abcaccabbacbcabaabaacabbbaabcbbbbacccaaabaacabbababbbbbcbcbbaaaabcaacbcccbabcaacaaabcbbcbbbcaabccacb\\n\", \"bbbbbbbbcccccccdddcdddddddddddeeeeeaaaddddddddddddddbbbbbbbbbbcccccccccddccccccbbcccccccdddddbdddddd\\n\", \"aaabaaccccccccdcccccaaaacccccccccccaaaaaacaaaaaaaabbbbaacccccccccccccccaaaaaaaaccccccbbbbbbbbccccccc\\n\", \"aabb\\n\", \"aabcaa\\n\"], \"outputs\": [\"2\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"12\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"11\\n\", \"8\\n\", \"3\\n\", \"26\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"7\\n\", \"6\\n\", \"4\\n\", \"14\\n\", \"4\\n\", \"8\\n\", \"2\\n\", \"27\\n\", \"2\\n\", \"9\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"2\\n\", \"2\\n\", \"27\\n\", \"7\\n\", \"9\\n\", \"12\\n\", \"15\\n\", \"10\\n\", \"5\\n\", \"7\\n\", \"2\\n\", \"12\\n\", \"3\\n\", \"28\\n\", \"17\\n\", \"10\\n\", \"7\\n\", \"5\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"12\\n\", \"0\\n\", \"11\\n\", \"27\\n\", \"3\\n\", \"2\\n\", \"9\\n\", \"6\\n\", \"15\\n\", \"8\\n\", \"5\\n\", \"5\\n\", \"17\\n\", \"9\\n\", \"12\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"28\\n\", \"7\\n\", \"27\\n\", \"3\\n\", \"7\\n\", \"4\\n\", \"26\\n\", \"4\\n\", \"2\\n\", \"8\\n\", \"14\\n\", \"5\\n\", \"2\\n\", \"7\\n\", \"12\\n\", \"0\\n\", \"1\\n\", \"3\\n\", \"10\\n\", \"7\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"12\\n\", \"0\\n\", \"8\\n\", \"27\\n\", \"1\\n\", \"9\\n\", \"6\\n\", \"15\\n\", \"17\\n\", \"3\\n\", \"25\\n\", \"26\\n\", \"14\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"8\\n\", \"5\\n\", \"6\\n\", \"9\\n\", \"12\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"3\\n\", \"7\\n\", \"4\\n\", \"26\\n\", \"4\\n\", \"2\\n\", \"8\\n\", \"5\\n\", \"2\\n\", \"7\\n\", \"12\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"10\\n\", \"7\\n\", \"5\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"5\\n\", \"14\\n\", \"0\\n\", \"8\\n\", \"27\\n\", \"1\\n\", \"2\\n\", \"9\\n\", \"6\\n\", \"2\\n\", \"1\\n\"]}", "dataset_type": "taco"} |
taco_7403 | deepcoder | Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
- Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
-----Constraints-----
- 2 \leq N \leq 10^{12}
- N is an integer.
-----Input-----
Input is given from Standard Input in the following format:
N
-----Output-----
Print the number of choices of K in which N becomes 1 in the end.
-----Sample Input-----
6
-----Sample Output-----
3
There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.
In each of these choices, N will change as follows:
- When K=2: 6 \to 3 \to 1
- When K=5: 6 \to 1
- When K=6: 6 \to 1 | {"ground_truth": "{\"inputs\": [\"6\\n\", \"3141\\n\", \"314159265358\\n\", \"1000000000000\\n\", \"642507465600\\n\", \"2\\n\", \"4294967296\\n\", \"260522\\n\", \"914575\\n\", \"436426\\n\", \"540024979445\\n\", \"917861648772\\n\", \"962623690081\\n\", \"523968956449\\n\", \"145329450841\\n\", \"2106351025\\n\", \"1056315001\\n\", \"953519049290\\n\", \"512385387722\\n\", \"32245025762\\n\", \"171518565905\\n\", \"77092338683\\n\", \"639098872693\\n\", \"674636966762\\n\", \"128016993662\\n\", \"7705668993\", \"2827\", \"6363881708\", \"2031\", \"10229584853\", \"308\", \"13543667986\", \"23472293460\", \"45468207033\", \"9\", \"5\", \"9717370676\", \"2\", \"4835308085\", \"5911967272\", \"10216071955\", \"71317993\", \"23778340\", \"30317876\", \"3276921\", \"2777701\", \"5099694\", \"9086817\", \"317623\", \"2481\", \"12173474602\", \"3\", \"16676667651\", \"1440741576\", \"409201\", \"27128790536\", \"2580169636\", \"11657801\", \"1151425\", \"79815666421\", \"2088751\", \"5905\", \"1221135085\", \"1969062355\", \"3602283174\", \"2935816\", \"34113\", \"1279233\", \"571234885\", \"1157731473\", \"3565\", \"1857\", \"162897857\", \"38799441\", \"303855297\", \"210161876\", \"75376\", \"5165510725\", \"27055\", \"1168644621\", \"6301\", \"10826961\", \"19377937\", \"109\", \"95\", \"48121289994\", \"6028372408\", \"10\", \"6082577109\", \"763370355\", \"838283426\", \"31903635\", \"41120962\", \"9523042\", \"3655901\", \"2533371\", \"1308265\", \"1821119\", \"3639573\", \"3363376\", \"2907971\", \"3461960\", \"3371400\", \"878316\", \"82922\", \"41587\", \"39008\", \"2193\", \"4017\", \"920\", \"1579\", \"124\", \"49\", \"14\", \"18\", \"34\", \"56\", \"54\", \"48\", \"79\", \"4\", \"16\", \"237274827109\", \"12\", \"2745\", \"314159265358\", \"6\", \"3141\"], \"outputs\": [\"3\\n\", \"13\\n\", \"9\\n\", \"266\\n\", \"12\\n\", \"1\\n\", \"37\\n\", \"9\\n\", \"8\\n\", \"37\\n\", \"12\\n\", \"7\\n\", \"96\\n\", \"385\\n\", \"289\\n\", \"42\\n\", \"161\\n\", \"4\\n\", \"4\\n\", \"28\\n\", \"76\\n\", \"16\\n\", \"48\\n\", \"3\\n\", \"3\\n\", \"64\\n\", \"12\\n\", \"17\\n\", \"16\\n\", \"6\\n\", \"4\\n\", \"33\\n\", \"11\\n\", \"48\\n\", \"5\\n\", \"3\\n\", \"14\\n\", \"1\\n\", \"24\\n\", \"9\\n\", \"49\\n\", \"32\\n\", \"10\\n\", \"18\\n\", \"65\\n\", \"72\\n\", \"7\\n\", \"25\\n\", \"8\\n\", \"20\\n\", \"13\\n\", \"2\\n\", \"98\\n\", \"51\\n\", \"120\\n\", \"66\\n\", \"50\\n\", \"96\\n\", \"42\\n\", \"144\\n\", \"40\\n\", \"31\\n\", \"36\\n\", \"73\\n\", \"19\\n\", \"34\\n\", \"29\\n\", \"37\\n\", \"97\\n\", \"41\\n\", \"30\\n\", \"15\\n\", \"56\\n\", \"81\\n\", \"28\\n\", \"62\\n\", \"26\\n\", \"192\\n\", \"22\\n\", \"121\\n\", \"54\\n\", \"80\\n\", \"60\\n\", \"12\\n\", \"4\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"12\\n\", \"6\\n\", \"49\\n\", \"9\\n\", \"17\\n\", \"9\\n\", \"18\\n\", \"16\\n\", \"48\\n\", \"16\\n\", \"12\\n\", \"17\\n\", \"16\\n\", \"6\\n\", \"5\\n\", \"5\\n\", \"6\\n\", \"17\\n\", \"5\\n\", \"10\\n\", \"11\\n\", \"3\\n\", \"8\\n\", \"5\\n\", \"11\\n\", \"3\\n\", \"3\\n\", \"5\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"8\\n\", \"3\\n\", \"6\\n\", \"24\\n\", \"4\\n\", \"16\\n\", \"9\", \"3\", \"13\"]}", "dataset_type": "taco"} |
taco_7404 | deepcoder | During a New Year special offer the "Sudislavl Bars" offered n promo codes. Each promo code consists of exactly six digits and gives right to one free cocktail at the bar "Mosquito Shelter". Of course, all the promocodes differ.
As the "Mosquito Shelter" opens only at 9, and partying in Sudislavl usually begins at as early as 6, many problems may arise as to how to type a promotional code without errors. It is necessary to calculate such maximum k, that the promotional code could be uniquely identified if it was typed with no more than k errors. At that, k = 0 means that the promotional codes must be entered exactly.
A mistake in this problem should be considered as entering the wrong numbers. For example, value "123465" contains two errors relative to promocode "123456". Regardless of the number of errors the entered value consists of exactly six digits.
-----Input-----
The first line of the output contains number n (1 ≤ n ≤ 1000) — the number of promocodes.
Each of the next n lines contains a single promocode, consisting of exactly 6 digits. It is guaranteed that all the promocodes are distinct. Promocodes can start from digit "0".
-----Output-----
Print the maximum k (naturally, not exceeding the length of the promocode), such that any promocode can be uniquely identified if it is typed with at most k mistakes.
-----Examples-----
Input
2
000000
999999
Output
2
Input
6
211111
212111
222111
111111
112111
121111
Output
0
-----Note-----
In the first sample k < 3, so if a bar customer types in value "090909", then it will be impossible to define which promocode exactly corresponds to it. | {"ground_truth": "{\"inputs\": [\"2\\n000000\\n999999\\n\", \"6\\n211111\\n212111\\n222111\\n111111\\n112111\\n121111\\n\", \"1\\n123456\\n\", \"2\\n000000\\n099999\\n\", \"2\\n000000\\n009999\\n\", \"2\\n000000\\n000999\\n\", \"2\\n000000\\n000099\\n\", \"2\\n000000\\n000009\\n\", \"1\\n000000\\n\", \"1\\n999999\\n\", \"10\\n946965\\n781372\\n029568\\n336430\\n456975\\n119377\\n179098\\n925374\\n878716\\n461563\\n\", \"10\\n878711\\n193771\\n965021\\n617901\\n333641\\n307811\\n989461\\n461561\\n956811\\n253741\\n\", \"10\\n116174\\n914694\\n615024\\n115634\\n717464\\n910984\\n513744\\n111934\\n915684\\n817874\\n\", \"10\\n153474\\n155468\\n151419\\n151479\\n158478\\n159465\\n150498\\n157416\\n150429\\n159446\\n\", \"10\\n141546\\n941544\\n141547\\n041542\\n641545\\n841547\\n941540\\n741544\\n941548\\n641549\\n\", \"10\\n114453\\n114456\\n114457\\n114450\\n114459\\n114451\\n114458\\n114452\\n114455\\n114454\\n\", \"5\\n145410\\n686144\\n859775\\n922809\\n470967\\n\", \"9\\n145410\\n686144\\n859775\\n922809\\n470967\\n234531\\n597023\\n318298\\n701652\\n\", \"10\\n145410\\n686144\\n859775\\n922809\\n470967\\n234531\\n597023\\n318298\\n701652\\n063386\\n\", \"20\\n145410\\n686144\\n766870\\n859775\\n922809\\n470967\\n034349\\n318920\\n019664\\n667953\\n295078\\n908733\\n691385\\n774622\\n325695\\n443254\\n817406\\n984471\\n512092\\n635832\\n\", \"50\\n145410\\n686144\\n766870\\n859775\\n922809\\n470967\\n034349\\n318920\\n019664\\n667953\\n295078\\n908733\\n691385\\n774622\\n325695\\n443254\\n817406\\n984471\\n512092\\n635832\\n303546\\n189826\\n128551\\n720334\\n569318\\n377719\\n281502\\n956352\\n758447\\n207280\\n583935\\n246631\\n160045\\n452683\\n594100\\n806017\\n232727\\n673001\\n799299\\n396463\\n061796\\n538266\\n947198\\n055121\\n080213\\n501424\\n600679\\n254914\\n872248\\n133173\\n\", 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\"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"2\", \"0\"]}", "dataset_type": "taco"} |
taco_7405 | deepcoder | For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | {"ground_truth": "{\"inputs\": [\"4\\n1 2 2 4\\n3\\n2\\n3\\n6\", \"4\\n1 1 2 4\\n3\\n0\\n3\\n8\", \"4\\n0 1 2 7\\n3\\n0\\n7\\n10\", \"4\\n0 1 2 6\\n3\\n0\\n3\\n6\", \"4\\n1 2 1 4\\n2\\n0\\n3\\n8\", \"4\\n0 1 2 7\\n1\\n0\\n5\\n3\", \"4\\n0 2 3 4\\n3\\n2\\n3\\n4\", \"4\\n0 1 2 7\\n1\\n-1\\n5\\n3\", \"4\\n0 2 1 3\\n3\\n-1\\n3\\n6\", \"4\\n0 2 2 1\\n3\\n4\\n3\\n0\", \"4\\n1 1 1 4\\n2\\n0\\n1\\n8\", \"4\\n0 0 2 5\\n2\\n0\\n3\\n4\", \"4\\n2 2 2 4\\n2\\n2\\n4\\n5\", \"4\\n-1 2 3 4\\n3\\n0\\n3\\n4\", \"4\\n0 2 2 4\\n3\\n2\\n3\\n5\", \"4\\n1 2 2 4\\n3\\n2\\n3\\n9\", \"4\\n0 2 2 4\\n3\\n4\\n3\\n5\", \"4\\n1 1 2 4\\n3\\n2\\n3\\n9\", \"4\\n1 1 2 4\\n3\\n2\\n3\\n8\", \"4\\n1 1 1 4\\n3\\n0\\n3\\n8\", \"4\\n1 1 1 4\\n3\\n0\\n3\\n6\", \"4\\n1 1 2 4\\n3\\n0\\n3\\n6\", \"4\\n0 1 2 4\\n3\\n0\\n3\\n6\", \"4\\n0 1 2 7\\n3\\n0\\n3\\n6\", \"4\\n0 1 2 7\\n3\\n0\\n5\\n6\", \"4\\n0 1 2 7\\n3\\n0\\n5\\n10\", \"4\\n0 0 2 7\\n3\\n0\\n7\\n10\", \"4\\n0 0 3 7\\n3\\n0\\n7\\n10\", \"4\\n2 2 2 4\\n3\\n2\\n3\\n5\", 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taco_7406 | deepcoder | Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a1, a2, ..., an are good.
Now she is interested in good sequences. A sequence x1, x2, ..., xk is called good if it satisfies the following three conditions:
* The sequence is strictly increasing, i.e. xi < xi + 1 for each i (1 ≤ i ≤ k - 1).
* No two adjacent elements are coprime, i.e. gcd(xi, xi + 1) > 1 for each i (1 ≤ i ≤ k - 1) (where gcd(p, q) denotes the greatest common divisor of the integers p and q).
* All elements of the sequence are good integers.
Find the length of the longest good sequence.
Input
The input consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 105) — the number of good integers. The second line contains a single-space separated list of good integers a1, a2, ..., an in strictly increasing order (1 ≤ ai ≤ 105; ai < ai + 1).
Output
Print a single integer — the length of the longest good sequence.
Examples
Input
5
2 3 4 6 9
Output
4
Input
9
1 2 3 5 6 7 8 9 10
Output
4
Note
In the first example, the following sequences are examples of good sequences: [2; 4; 6; 9], [2; 4; 6], [3; 9], [6]. The length of the longest good sequence is 4. | {"ground_truth": "{\"inputs\": [\"2\\n1009 2018\\n\", \"7\\n1 2 3 4 7 9 10\\n\", \"2\\n601 1202\\n\", \"8\\n3 4 5 6 7 8 9 10\\n\", \"2\\n5101 10202\\n\", \"3\\n21 67 243\\n\", \"5\\n2 3 7 9 10\\n\", \"1\\n99991\\n\", \"3\\n1 4 7\\n\", \"3\\n3 14 22\\n\", \"10\\n2 4 8 67 128 324 789 1296 39877 98383\\n\", \"10\\n2 3 45 67 89 101 234 567 890 1234\\n\", \"3\\n150 358 382\\n\", \"1\\n1\\n\", \"4\\n1 2 4 6\\n\", \"10\\n2 3 4 5 6 7 8 9 10 11\\n\", \"9\\n1 2 3 4 5 6 7 9 10\\n\", \"10\\n1 2 4 8 16 32 33 64 128 256\\n\", \"10\\n2 3 10 40 478 3877 28787 88888 99999 100000\\n\", \"10\\n2 3 4 5 6 8 9 10 17 92\\n\", \"1\\n4\\n\", \"10\\n13 2187 2197 4567 5200 29873 67866 98798 99999 100000\\n\", \"44\\n1 5 37 97 107 147 185 187 195 241 249 295 311 323 341 345 363 391 425 431 473 525 539 541 555 577 595 611 647 695 757 759 775 779 869 877 927 935 963 965 967 969 973 975\\n\", \"49\\n10 34 58 72 126 166 176 180 198 200 208 228 238 248 302 332 340 344 350 354 380 406 418 428 438 442 482 532 536 544 546 554 596 626 642 682 684 704 714 792 804 820 862 880 906 946 954 966 970\\n\", \"2\\n1361 2018\\n\", \"2\\n20 1202\\n\", \"8\\n3 4 5 5 7 8 9 10\\n\", \"10\\n2 4 8 67 128 324 191 1296 39877 98383\\n\", \"10\\n2 3 30 67 89 101 234 567 890 1234\\n\", \"10\\n13 2187 2197 4567 2258 29873 67866 98798 99999 100000\\n\", \"10\\n2 4 8 67 128 324 191 2298 50122 98383\\n\", \"2\\n6108 10202\\n\", \"3\\n17 67 243\\n\", \"5\\n2 4 7 9 10\\n\", \"1\\n97661\\n\", \"3\\n1 4 11\\n\", \"3\\n1 14 22\\n\", \"3\\n150 358 633\\n\", \"1\\n2\\n\", \"4\\n1 1 4 6\\n\", \"10\\n2 3 4 5 6 8 9 10 25 92\\n\", \"1\\n8\\n\", \"5\\n2 3 4 6 7\\n\", \"2\\n39 1202\\n\", \"2\\n5026 10202\\n\", \"3\\n17 52 243\\n\", \"5\\n2 4 7 9 20\\n\", \"3\\n1 7 11\\n\", \"3\\n1 10 22\\n\", \"10\\n2 4 8 67 128 324 191 2298 39877 98383\\n\", \"10\\n2 3 30 67 91 101 234 567 890 1234\\n\", \"3\\n150 358 488\\n\", \"1\\n3\\n\", \"4\\n1 2 5 6\\n\", \"10\\n2 3 4 5 6 8 9 1 25 92\\n\", \"1\\n7\\n\", \"5\\n2 3 4 6 13\\n\", \"2\\n7791 10202\\n\", \"3\\n17 52 332\\n\", \"5\\n2 7 7 9 20\\n\", \"10\\n2 3 34 67 91 101 234 567 890 1234\\n\", \"1\\n9\\n\", \"10\\n2 3 4 5 3 8 9 1 25 92\\n\", \"1\\n6\\n\", \"2\\n5295 10202\\n\", \"3\\n17 19 332\\n\", \"5\\n2 7 7 9 27\\n\", \"10\\n2 4 8 67 200 324 191 2298 50122 98383\\n\", \"10\\n2 3 34 67 81 101 234 567 890 1234\\n\", \"1\\n10\\n\", \"1\\n5\\n\", \"2\\n6253 10202\\n\", \"3\\n10 19 332\\n\", \"10\\n2 4 8 67 200 391 191 2298 50122 98383\\n\", \"1\\n16\\n\", \"1\\n14\\n\", \"2\\n6253 16319\\n\", \"10\\n2 4 8 67 200 391 379 2298 50122 98383\\n\", \"1\\n27\\n\", \"9\\n1 2 3 5 6 7 8 9 10\\n\", \"5\\n2 3 4 6 9\\n\"], \"outputs\": [\"2\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"8\\n\", \"6\\n\", \"6\\n\", \"1\\n\", \"6\\n\", \"15\\n\", \"49\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"7\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"4\\n\", \"4\\n\"]}", "dataset_type": "taco"} |
taco_7407 | deepcoder | Polycarp knows that if the sum of the digits of a number is divisible by $3$, then the number itself is divisible by $3$. He assumes that the numbers, the sum of the digits of which is divisible by $4$, are also somewhat interesting. Thus, he considers a positive integer $n$ interesting if its sum of digits is divisible by $4$.
Help Polycarp find the nearest larger or equal interesting number for the given number $a$. That is, find the interesting number $n$ such that $n \ge a$ and $n$ is minimal.
-----Input-----
The only line in the input contains an integer $a$ ($1 \le a \le 1000$).
-----Output-----
Print the nearest greater or equal interesting number for the given number $a$. In other words, print the interesting number $n$ such that $n \ge a$ and $n$ is minimal.
-----Examples-----
Input
432
Output
435
Input
99
Output
103
Input
237
Output
237
Input
42
Output
44 | {"ground_truth": "{\"inputs\": [\"432\\n\", \"99\\n\", \"237\\n\", \"42\\n\", \"1\\n\", \"2\\n\", \"1000\\n\", \"898\\n\", \"997\\n\", \"999\\n\", \"399\\n\", \"8\\n\", \"120\\n\", \"909\\n\", \"9\\n\", \"398\\n\", \"7\\n\", \"799\\n\", \"970\\n\", \"188\\n\", \"4\\n\", \"38\\n\", \"12\\n\", \"3\\n\", \"518\\n\", \"6\\n\", \"400\\n\", \"36\\n\", \"398\\n\", \"909\\n\", \"120\\n\", \"399\\n\", \"1\\n\", \"997\\n\", \"400\\n\", \"6\\n\", \"518\\n\", \"799\\n\", \"3\\n\", \"999\\n\", \"36\\n\", \"9\\n\", \"970\\n\", \"1000\\n\", \"8\\n\", \"12\\n\", \"4\\n\", \"2\\n\", \"898\\n\", \"188\\n\", \"38\\n\", \"7\\n\", \"184\\n\", \"223\\n\", \"130\\n\", \"242\\n\", \"441\\n\", \"704\\n\", \"60\\n\", \"5\\n\", \"79\\n\", \"14\\n\", \"22\\n\", \"479\\n\", \"269\\n\", \"13\\n\", \"24\\n\", \"100\\n\", \"861\\n\", \"275\\n\", \"355\\n\", \"83\\n\", \"410\\n\", \"417\\n\", \"37\\n\", \"71\\n\", \"246\\n\", \"300\\n\", \"43\\n\", \"979\\n\", \"207\\n\", \"550\\n\", \"112\\n\", \"107\\n\", \"603\\n\", \"171\\n\", \"457\\n\", \"962\\n\", \"407\\n\", \"162\\n\", \"189\\n\", \"575\\n\", \"155\\n\", \"27\\n\", \"55\\n\", \"422\\n\", \"614\\n\", \"376\\n\", \"903\\n\", \"284\\n\", \"505\\n\", \"601\\n\", \"34\\n\", \"396\\n\", \"74\\n\", \"461\\n\", \"711\\n\", \"660\\n\", \"508\\n\", \"51\\n\", \"215\\n\", \"320\\n\", \"262\\n\", \"748\\n\", \"684\\n\", \"94\\n\", \"45\\n\", \"429\\n\", \"390\\n\", \"693\\n\", \"103\\n\", \"15\\n\", \"39\\n\", \"69\\n\", \"26\\n\", \"23\\n\", \"44\\n\", \"11\\n\", \"222\\n\", \"10\\n\", \"41\\n\", \"67\\n\", \"20\\n\", \"17\\n\", \"19\\n\", \"18\\n\", \"358\\n\", \"58\\n\", \"163\\n\", \"16\\n\", \"185\\n\", \"32\\n\", \"31\\n\", \"50\\n\", \"102\\n\", \"99\\n\", \"432\\n\", \"237\\n\", \"42\\n\"], \"outputs\": [\"435\\n\", \"103\\n\", \"237\\n\", \"44\\n\", \"4\\n\", \"4\\n\", \"1003\\n\", \"903\\n\", \"1003\\n\", \"1003\\n\", \"400\\n\", \"8\\n\", \"121\\n\", \"912\\n\", \"13\\n\", \"398\\n\", \"8\\n\", \"800\\n\", \"970\\n\", \"192\\n\", \"4\\n\", \"39\\n\", \"13\\n\", \"4\\n\", \"521\\n\", \"8\\n\", \"400\\n\", \"39\\n\", \"398\\n\", \"912\\n\", \"121\\n\", \"400\\n\", \"4\\n\", \"1003\\n\", \"400\\n\", \"8\\n\", \"521\\n\", \"800\\n\", \"4\\n\", \"1003\\n\", \"39\\n\", \"13\\n\", \"970\\n\", \"1003\\n\", \"8\\n\", \"13\\n\", \"4\\n\", \"4\\n\", \"903\\n\", \"192\\n\", \"39\\n\", \"8\\n\", \"187\\n\", \"224\\n\", \"130\\n\", \"242\\n\", \"444\\n\", \"705\\n\", \"62\\n\", \"8\\n\", \"79\\n\", \"17\\n\", \"22\\n\", \"479\\n\", \"273\\n\", \"13\\n\", \"26\\n\", \"103\\n\", \"862\\n\", \"277\\n\", \"358\\n\", \"84\\n\", \"413\\n\", \"417\\n\", \"39\\n\", \"71\\n\", \"246\\n\", \"301\\n\", \"44\\n\", \"983\\n\", \"211\\n\", \"552\\n\", \"112\\n\", \"107\\n\", \"606\\n\", \"174\\n\", \"457\\n\", \"965\\n\", \"408\\n\", \"165\\n\", \"192\\n\", \"578\\n\", \"156\\n\", \"31\\n\", \"57\\n\", \"422\\n\", \"615\\n\", \"376\\n\", \"903\\n\", \"286\\n\", \"507\\n\", \"602\\n\", \"35\\n\", \"398\\n\", \"75\\n\", \"462\\n\", \"714\\n\", \"660\\n\", \"512\\n\", \"53\\n\", \"215\\n\", \"323\\n\", \"264\\n\", \"749\\n\", \"686\\n\", \"97\\n\", \"48\\n\", \"431\\n\", \"390\\n\", \"695\\n\", \"103\\n\", \"17\\n\", \"39\\n\", \"71\\n\", \"26\\n\", \"26\\n\", \"44\\n\", \"13\\n\", \"224\\n\", \"13\\n\", \"44\\n\", \"71\\n\", \"22\\n\", \"17\\n\", \"22\\n\", \"22\\n\", \"358\\n\", \"62\\n\", \"165\\n\", \"17\\n\", \"187\\n\", \"35\\n\", \"31\\n\", \"53\\n\", \"103\\n\", \"103\\n\", \"435\\n\", \"237\\n\", \"44\\n\"]}", "dataset_type": "taco"} |
taco_7408 | deepcoder | Takahashi has A untasty cookies containing antidotes, B tasty cookies containing antidotes and C tasty cookies containing poison.
Eating a cookie containing poison results in a stomachache, and eating a cookie containing poison while having a stomachache results in a death. As he wants to live, he cannot eat one in such a situation. Eating a cookie containing antidotes while having a stomachache cures it, and there is no other way to cure stomachaches.
Find the maximum number of tasty cookies that Takahashi can eat.
Constraints
* 0 \leq A,B,C \leq 10^9
* A,B and C are integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the maximum number of tasty cookies that Takahashi can eat.
Examples
Input
3 1 4
Output
5
Input
5 2 9
Output
10
Input
8 8 1
Output
9 | {"ground_truth": "{\"inputs\": [\"0 1 4\", \"14 8 1\", \"9 2 9\", \"0 0 4\", \"14 8 2\", \"3 2 9\", \"11 15 2\", \"11 15 4\", \"3 0 12\", \"0 2 0\", \"11 15 0\", \"0 0 0\", \"16 5 0\", \"-2 0 0\", \"3 1 27\", \"-1 1 -4\", \"6 -2 0\", \"-1 -2 0\", \"-2 -2 -1\", \"-4 -2 -1\", \"0 -2 -4\", \"0 -2 -6\", \"1 -8 7\", \"1 -10 20\", \"0 -8 5\", \"-1 -1 -8\", \"-1 -2 -8\", \"-1 -3 -8\", \"-1 -3 -9\", \"2 10 2\", \"2 10 4\", \"0 -9 -1\", \"0 -11 -2\", \"0 -10 -2\", \"0 -18 -2\", \"-1 -18 -1\", \"-2 -18 -1\", \"-2 -24 -1\", \"0 -24 0\", \"-1 -24 0\", \"-1 -20 0\", \"-14 0 -2\", \"-2 -20 -1\", \"-3 -20 -1\", \"-21 -1 -2\", \"-3 -15 -1\", \"-3 -18 -1\", \"-3 -25 -1\", \"-5 -25 -1\", \"-2 -25 -1\", \"-3 -7 4\", \"-4 -25 -1\", \"-2 -49 -4\", \"-2 -74 -4\", \"-2 -82 -4\", \"-2 -101 -9\", \"-1 -101 -1\", \"0 -101 -1\", \"0 -23 -1\", \"-1 -23 -1\", \"2 26 -10\", \"2 2 9\", \"-1 -17 1\", \"-1 1 -31\", \"-1 -28 4\", \"-2 -28 4\", \"-14 0 -28\", \"-14 0 -25\", \"-14 1 -25\", \"-16 1 -32\", \"-3 -1 -22\", \"-3 -24 -1\", \"-3 -9 -1\", \"0 17 1\", \"0 20 1\", \"0 20 0\", \"1 22 0\", \"-1 1 -64\", \"-1 1 -67\", \"-1 1 -27\", \"-1 1 -45\", \"1 0 -84\", \"1 0 -131\", \"3 14 -1\", \"1 0 -73\", \"1 0 -91\", \"1 0 -60\", \"1 0 -98\", \"1 -2 -98\", \"1 -2 -180\", \"-2 24 -1\", \"1 -2 -143\", \"1 -3 -143\", \"-1 -5 -143\", \"0 -5 -167\", \"0 -1 -167\", \"0 -20 0\", \"1 -1 -220\", \"1 -1 -348\", \"-1 -37 0\", \"3 1 4\", \"8 8 1\", \"5 2 9\"], \"outputs\": [\"3\\n\", \"9\\n\", \"11\\n\", \"1\\n\", \"10\\n\", \"8\\n\", \"17\\n\", \"19\\n\", \"4\\n\", \"2\\n\", \"15\\n\", \"0\\n\", \"5\\n\", \"-1\\n\", \"6\\n\", \"-3\\n\", \"-2\\n\", \"-4\\n\", \"-5\\n\", \"-7\\n\", \"-6\\n\", \"-8\\n\", \"-14\\n\", \"-18\\n\", \"-15\\n\", \"-9\\n\", \"-10\\n\", \"-11\\n\", \"-12\\n\", \"12\\n\", \"14\\n\", \"-17\\n\", \"-21\\n\", \"-19\\n\", \"-35\\n\", \"-36\\n\", \"-37\\n\", \"-49\\n\", \"-47\\n\", \"-48\\n\", \"-40\\n\", \"-13\\n\", \"-41\\n\", \"-42\\n\", \"-22\\n\", \"-32\\n\", \"-38\\n\", \"-52\\n\", \"-54\\n\", \"-51\\n\", \"-16\\n\", \"-53\\n\", \"-99\\n\", \"-149\\n\", \"-165\\n\", \"-203\\n\", \"-202\\n\", \"-201\\n\", \"-45\\n\", \"-46\\n\", \"16\\n\", \"7\\n\", \"-34\\n\", \"-30\\n\", \"-56\\n\", \"-57\\n\", \"-28\\n\", \"-25\\n\", \"-24\\n\", \"-31\\n\", \"-23\\n\", \"-50\\n\", \"-20\\n\", \"18\\n\", \"21\\n\", \"20\\n\", \"22\\n\", \"-63\\n\", \"-66\\n\", \"-26\\n\", \"-44\\n\", \"-84\\n\", \"-131\\n\", \"13\\n\", \"-73\\n\", \"-91\\n\", \"-60\\n\", \"-98\\n\", \"-100\\n\", \"-182\\n\", \"23\\n\", \"-145\\n\", \"-146\\n\", \"-148\\n\", \"-172\\n\", \"-168\\n\", \"-39\\n\", \"-221\\n\", \"-349\\n\", \"-74\\n\", \"5\", \"9\", \"10\"]}", "dataset_type": "taco"} |
taco_7409 | deepcoder | In the Kingdom of AtCoder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1, 10, 10^2, 10^3, \dots, 10^{(10^{100})}. You have come shopping at a mall and are now buying a takoyaki machine with a value of N. (Takoyaki is the name of a Japanese snack.)
To make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N.
What will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count?
Assume that you have sufficient numbers of banknotes, and so does the clerk.
-----Constraints-----
- N is an integer between 1 and 10^{1,000,000} (inclusive).
-----Input-----
Input is given from Standard Input in the following format:
N
-----Output-----
Print the minimum possible number of total banknotes used by you and the clerk.
-----Sample Input-----
36
-----Sample Output-----
8
If you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used.
The payment cannot be made with less than eight banknotes in total, so the answer is 8. | {"ground_truth": "{\"inputs\": [\"36\\n\", \"91\\n\", \"314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170\\n\", \"30\", \"476640020082194381531155118436783393866726953614433851622190777875571135215042541028243752681838573\", \"22\", \"41\", \"402419059500366785869358882282163159674165660152915334404536663378232442791064106232595577577780162\", \"85935701773254562628410719372396848335402648590418634844101760809881540580187751784321748296967820\", \"112971229910948442277742063793860536302679259212406616014111988669828741066875057785985507004364571\", \"9\", \"112951179209792539124037565379106363289174458264689808441706471502486080445534951144969723896577005\", \"30635919304419657545615271990396525521219360923496828845301606010256650094809182113049943540395907\", 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\"314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170\", \"36\"], \"outputs\": [\"8\\n\", \"3\\n\", \"243\\n\", \"3\\n\", \"259\\n\", \"4\\n\", \"5\\n\", \"252\\n\", \"243\\n\", \"225\\n\", \"2\\n\", \"246\\n\", \"235\\n\", \"221\\n\", \"237\\n\", \"244\\n\", \"220\\n\", \"227\\n\", \"224\\n\", \"216\\n\", \"232\\n\", \"238\\n\", \"251\\n\", \"239\\n\", \"261\\n\", \"255\\n\", \"231\\n\", \"257\\n\", \"272\\n\", \"242\\n\", \"236\\n\", \"228\\n\", \"240\\n\", \"253\\n\", \"248\\n\", \"260\\n\", \"249\\n\", \"214\\n\", \"265\\n\", \"258\\n\", \"263\\n\", \"230\\n\", \"213\\n\", \"218\\n\", \"245\\n\", \"233\\n\", \"241\\n\", \"223\\n\", \"250\\n\", \"234\\n\", \"247\\n\", \"209\\n\", \"226\\n\", \"267\\n\", \"256\\n\", \"200\\n\", \"210\\n\", \"179\\n\", \"204\\n\", \"215\\n\", \"189\\n\", \"198\\n\", \"196\\n\", \"211\\n\", \"208\\n\", \"201\\n\", \"195\\n\", \"202\\n\", \"205\\n\", \"222\\n\", \"219\\n\", \"194\\n\", \"212\\n\", \"199\\n\", \"180\\n\", \"188\\n\", \"187\\n\", \"203\\n\", \"207\\n\", \"177\\n\", \"191\\n\", \"206\\n\", \"182\\n\", \"192\\n\", \"229\\n\", \"193\\n\", \"197\\n\", \"217\\n\", \"186\\n\", \"172\\n\", \"174\\n\", \"185\\n\", \"183\\n\", \"181\\n\", \"170\\n\", \"173\\n\", \"178\\n\", \"190\\n\", \"176\\n\", \"158\\n\", \"163\\n\", \"161\\n\", \"171\\n\", \"3\", \"243\", \"8\"]}", "dataset_type": "taco"} |
taco_7410 | deepcoder | Bob has a favorite number k and ai of length n. Now he asks you to answer m queries. Each query is given by a pair li and ri and asks you to count the number of pairs of integers i and j, such that l ≤ i ≤ j ≤ r and the xor of the numbers ai, ai + 1, ..., aj is equal to k.
Input
The first line of the input contains integers n, m and k (1 ≤ n, m ≤ 100 000, 0 ≤ k ≤ 1 000 000) — the length of the array, the number of queries and Bob's favorite number respectively.
The second line contains n integers ai (0 ≤ ai ≤ 1 000 000) — Bob's array.
Then m lines follow. The i-th line contains integers li and ri (1 ≤ li ≤ ri ≤ n) — the parameters of the i-th query.
Output
Print m lines, answer the queries in the order they appear in the input.
Examples
Input
6 2 3
1 2 1 1 0 3
1 6
3 5
Output
7
0
Input
5 3 1
1 1 1 1 1
1 5
2 4
1 3
Output
9
4
4
Note
In the first sample the suitable pairs of i and j for the first query are: (1, 2), (1, 4), (1, 5), (2, 3), (3, 6), (5, 6), (6, 6). Not a single of these pairs is suitable for the second query.
In the second sample xor equals 1 for all subarrays of an odd length. | {"ground_truth": "{\"inputs\": [\"6 2 4\\n1 2 1 1 0 3\\n1 6\\n3 5\\n\", \"5 3 1\\n0 1 1 1 1\\n1 5\\n2 4\\n1 3\\n\", \"6 2 3\\n1 4 1 1 0 3\\n1 6\\n3 5\\n\", \"5 3 1\\n0 1 1 1 1\\n1 5\\n2 4\\n1 2\\n\", \"5 3 0\\n0 1 1 1 1\\n1 5\\n2 4\\n1 2\\n\", \"6 2 4\\n1 2 1 1 1 5\\n1 6\\n3 5\\n\", \"5 3 1\\n0 1 2 1 1\\n1 5\\n2 4\\n1 2\\n\", \"5 3 1\\n0 1 2 1 1\\n1 5\\n3 4\\n1 2\\n\", \"6 2 3\\n1 2 0 1 0 3\\n1 6\\n3 5\\n\", \"5 3 1\\n1 1 1 1 1\\n1 5\\n2 2\\n1 3\\n\", \"5 3 1\\n0 1 1 1 2\\n1 5\\n2 4\\n1 2\\n\", \"6 2 3\\n1 4 1 2 0 3\\n1 6\\n2 5\\n\", \"5 3 0\\n0 1 1 1 1\\n1 5\\n1 4\\n1 2\\n\", \"6 2 7\\n1 2 1 1 1 5\\n1 6\\n3 5\\n\", \"6 2 1\\n1 2 0 1 0 3\\n1 6\\n3 5\\n\", \"5 3 1\\n1 1 1 2 1\\n1 5\\n2 2\\n1 3\\n\", \"5 3 1\\n0 1 1 1 2\\n1 1\\n2 4\\n1 2\\n\", \"6 2 3\\n1 4 1 2 0 3\\n1 4\\n2 5\\n\", \"5 3 1\\n1 1 1 2 1\\n2 5\\n2 2\\n1 3\\n\", \"6 2 3\\n1 4 1 2 1 3\\n1 6\\n2 5\\n\", \"5 3 1\\n1 2 1 2 1\\n2 5\\n2 2\\n1 3\\n\", \"6 2 4\\n1 2 1 1 1 3\\n1 6\\n3 5\\n\", \"6 2 4\\n2 2 1 1 1 3\\n1 6\\n3 5\\n\", \"6 2 3\\n1 4 1 1 0 3\\n1 6\\n2 5\\n\", \"6 2 4\\n1 2 1 1 1 5\\n1 6\\n3 0\\n\", \"6 2 4\\n0 2 1 1 0 3\\n1 6\\n3 5\\n\", \"6 2 4\\n1 0 1 1 1 3\\n1 6\\n3 5\\n\", \"6 2 3\\n1 4 1 1 0 3\\n1 5\\n3 5\\n\", \"6 2 4\\n2 2 1 1 1 2\\n1 6\\n3 5\\n\", \"6 2 4\\n1 1 1 1 1 5\\n1 6\\n3 0\\n\", \"5 3 1\\n0 1 2 1 0\\n1 5\\n3 4\\n1 2\\n\", \"6 2 4\\n0 2 1 1 0 3\\n1 6\\n1 5\\n\", \"6 2 4\\n1 0 2 1 1 3\\n1 6\\n3 5\\n\", \"6 2 4\\n2 2 1 1 1 2\\n1 6\\n3 0\\n\", \"6 2 7\\n1 2 1 1 1 5\\n1 6\\n3 0\\n\", \"6 2 1\\n1 2 0 1 0 3\\n1 6\\n3 3\\n\", \"6 2 4\\n1 0 2 0 1 3\\n1 6\\n3 5\\n\", \"6 2 4\\n2 2 1 0 1 2\\n1 6\\n3 0\\n\", \"6 2 7\\n1 2 1 2 1 5\\n1 6\\n3 0\\n\", \"6 2 1\\n1 2 0 1 0 3\\n1 6\\n2 3\\n\", \"6 2 4\\n2 0 2 0 1 3\\n1 6\\n3 5\\n\", \"6 2 3\\n1 6 1 2 1 3\\n1 6\\n2 5\\n\", \"5 3 1\\n1 3 1 2 1\\n2 5\\n2 2\\n1 3\\n\", \"6 2 3\\n1 2 1 1 0 3\\n1 6\\n3 5\\n\", \"5 3 1\\n1 1 1 1 1\\n1 5\\n2 4\\n1 3\\n\"], \"outputs\": [\"0\\n0\\n\", \"8\\n4\\n3\\n\", \"3\\n0\\n\", \"8\\n4\\n2\\n\", \"7\\n2\\n1\\n\", \"2\\n0\\n\", \"4\\n2\\n2\\n\", \"4\\n1\\n2\\n\", \"6\\n0\\n\", \"9\\n1\\n4\\n\", \"6\\n4\\n2\\n\", \"4\\n2\\n\", \"7\\n4\\n1\\n\", \"1\\n0\\n\", \"6\\n4\\n\", \"5\\n1\\n4\\n\", \"0\\n4\\n2\\n\", \"1\\n2\\n\", \"3\\n1\\n4\\n\", \"3\\n2\\n\", \"3\\n0\\n2\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"3\\n0\\n\", \"2\\n0\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"3\\n0\\n\", \"4\\n1\\n2\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"1\\n0\\n\", \"6\\n0\\n\", \"0\\n0\\n\", \"0\\n0\\n\", \"1\\n0\\n\", \"6\\n0\\n\", \"0\\n0\\n\", \"3\\n2\\n\", \"3\\n0\\n2\\n\", \"7\\n0\\n\", \"9\\n4\\n4\\n\"]}", "dataset_type": "taco"} |
taco_7411 | deepcoder | Let's denote a function $f(x)$ in such a way: we add $1$ to $x$, then, while there is at least one trailing zero in the resulting number, we remove that zero. For example, $f(599) = 6$: $599 + 1 = 600 \rightarrow 60 \rightarrow 6$; $f(7) = 8$: $7 + 1 = 8$; $f(9) = 1$: $9 + 1 = 10 \rightarrow 1$; $f(10099) = 101$: $10099 + 1 = 10100 \rightarrow 1010 \rightarrow 101$.
We say that some number $y$ is reachable from $x$ if we can apply function $f$ to $x$ some (possibly zero) times so that we get $y$ as a result. For example, $102$ is reachable from $10098$ because $f(f(f(10098))) = f(f(10099)) = f(101) = 102$; and any number is reachable from itself.
You are given a number $n$; your task is to count how many different numbers are reachable from $n$.
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 10^9$).
-----Output-----
Print one integer: the number of different numbers that are reachable from $n$.
-----Examples-----
Input
1098
Output
20
Input
10
Output
19
-----Note-----
The numbers that are reachable from $1098$ are:
$1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1098, 1099$. | {"ground_truth": "{\"inputs\": [\"1098\\n\", \"10\\n\", \"1000000000\\n\", \"1\\n\", \"9\\n\", \"10119\\n\", \"1337\\n\", \"51\\n\", \"99\\n\", \"79\\n\", \"29\\n\", \"633\\n\", \"9000\\n\", \"99999999\\n\", \"932415950\\n\", \"90\\n\", \"45\\n\", \"22\\n\", \"987654321\\n\", \"599\\n\", \"54\\n\", \"73180\\n\", \"9392\\n\", \"25659427\\n\", \"1999\\n\", \"712\\n\", \"21\\n\", \"916073472\\n\", \"920\\n\", \"61261142\\n\", \"999999999\\n\", \"30\\n\", \"299\\n\", \"20\\n\", \"960879599\\n\", \"41\\n\", \"9590\\n\", \"9169813\\n\", \"2001\\n\", \"6171\\n\", \"23\\n\", \"99932791\\n\", \"959590\\n\", \"90000001\\n\", \"98\\n\", \"442188277\\n\", \"751780\\n\", \"909590\\n\", \"91\\n\", \"89\\n\", \"76\\n\", \"34\\n\", \"70\\n\", \"38\\n\", \"58\\n\", \"852240\\n\", \"94\\n\", \"44\\n\", \"83\\n\", \"81\\n\", \"49\\n\", \"71\\n\", \"204907\\n\", \"3\\n\", \"40\\n\", \"123123124\\n\", \"88\\n\", \"97\\n\", \"642853\\n\", \"986792\\n\", \"5\\n\", \"73\\n\", \"50\\n\", \"556740\\n\", \"259835150\\n\", \"5932\\n\", \"36\\n\", \"96\\n\", \"999999\\n\", \"921280\\n\", \"84\\n\", \"19909590\\n\", \"599785072\\n\", \"303719549\\n\", \"90909590\\n\", \"940160238\\n\", \"255\\n\", \"439674440\\n\", \"870826420\\n\", \"93\\n\", \"55\\n\", \"631\\n\", \"24\\n\", \"59\\n\", \"78\\n\", \"997184\\n\", \"189070\\n\", \"46\\n\", \"63\\n\", \"869667992\\n\", \"963\\n\", \"86\\n\", \"880708\\n\", \"80\\n\", \"902826\\n\", \"57\\n\", \"956126\\n\", \"790643\\n\", \"68\\n\", \"990\\n\", \"860082635\\n\", \"940740\\n\", \"87\\n\", \"799170\\n\", \"75\\n\", \"19\\n\", \"312770\\n\", \"69\\n\", \"855520\\n\", \"53\\n\", \"841480\\n\", \"60\\n\", \"196530\\n\", \"883260\\n\", \"962131\\n\", \"77\\n\", \"47\\n\", \"62\\n\", \"2333\\n\", \"999999970\\n\", \"97\\n\", \"36\\n\", \"855520\\n\", \"956126\\n\", \"439674440\\n\", \"990\\n\", \"30\\n\", \"69\\n\", \"38\\n\", \"196530\\n\", \"599785072\\n\", \"999999970\\n\", \"73180\\n\", \"920\\n\", \"21\\n\", \"9169813\\n\", \"40\\n\", \"83\\n\", \"962131\\n\", \"58\\n\", \"99932791\\n\", \"20\\n\", \"86\\n\", \"54\\n\", \"916073472\\n\", \"902826\\n\", \"642853\\n\", \"9590\\n\", \"41\\n\", \"59\\n\", \"77\\n\", \"963\\n\", \"999999\\n\", \"47\\n\", \"94\\n\", \"1000000000\\n\", \"88\\n\", \"997184\\n\", \"5\\n\", \"22\\n\", \"932415950\\n\", \"880708\\n\", \"841480\\n\", \"45\\n\", \"79\\n\", \"62\\n\", \"34\\n\", \"959590\\n\", \"633\\n\", \"9000\\n\", \"556740\\n\", \"940740\\n\", \"204907\\n\", \"870826420\\n\", \"10119\\n\", \"98\\n\", \"986792\\n\", \"189070\\n\", \"53\\n\", \"1\\n\", \"940160238\\n\", \"87\\n\", \"442188277\\n\", \"78\\n\", \"91\\n\", \"24\\n\", \"44\\n\", \"255\\n\", \"71\\n\", \"60\\n\", \"51\\n\", \"2001\\n\", \"19\\n\", \"99999999\\n\", \"68\\n\", \"55\\n\", \"303719549\\n\", \"61261142\\n\", \"123123124\\n\", \"6171\\n\", \"23\\n\", \"1999\\n\", \"70\\n\", \"883260\\n\", \"50\\n\", \"312770\\n\", \"81\\n\", \"712\\n\", \"84\\n\", \"799170\\n\", \"93\\n\", \"790643\\n\", \"921280\\n\", \"89\\n\", \"80\\n\", \"96\\n\", \"9\\n\", \"909590\\n\", \"860082635\\n\", \"5932\\n\", \"73\\n\", \"960879599\\n\", \"631\\n\", \"259835150\\n\", \"9392\\n\", \"90000001\\n\", \"19909590\\n\", \"29\\n\", \"987654321\\n\", \"599\\n\", \"76\\n\", \"2333\\n\", \"25659427\\n\", \"299\\n\", \"751780\\n\", \"3\\n\", \"90909590\\n\", \"869667992\\n\", \"999999999\\n\", \"1337\\n\", \"90\\n\", \"57\\n\", \"75\\n\", \"852240\\n\", \"99\\n\", \"49\\n\", \"46\\n\", \"63\\n\", \"39\\n\", \"33\\n\", \"51192\\n\", \"1661745\\n\", \"793468350\\n\", \"715\\n\", \"14\\n\", \"135\\n\", \"31\\n\", \"364565\\n\", \"1472811722\\n\", \"90781\\n\", \"6\\n\", \"2504450\\n\", \"15\\n\", \"1749822\\n\", \"184056476\\n\", \"16\\n\", \"17\\n\", \"1660033091\\n\", \"670161\\n\", \"1060421\\n\", \"8819\\n\", \"28\\n\", \"12\\n\", \"825\\n\", \"782980\\n\", \"1100000000\\n\", \"1059565\\n\", \"770459503\\n\", \"1275455\\n\", \"1053746\\n\", \"131\\n\", \"150309\\n\", \"4543\\n\", \"218479\\n\", \"589990244\\n\", \"123\\n\", \"109252064\\n\", \"1534054\\n\", \"1516433257\\n\", \"355091082\\n\", \"200229961\\n\", \"9114\\n\", \"11850851\\n\", \"398876344\\n\", \"1674\\n\", \"11\\n\", \"7\\n\", \"2\\n\", \"64\\n\", \"85\\n\", \"152\\n\", \"13\\n\", \"8\\n\", \"42\\n\", \"118\\n\", \"18\\n\", \"1262597\\n\", \"188\\n\", \"11372\\n\", \"822351\\n\", \"136156\\n\", \"836706360\\n\", \"143\\n\", \"1005296\\n\", \"103\\n\", \"826291891\\n\", \"4\\n\", \"56\\n\", \"27\\n\", \"336\\n\", \"107\\n\", \"35\\n\", \"48\\n\", \"398\\n\", \"26\\n\", \"127\\n\", \"360082507\\n\", \"51492957\\n\", \"45021689\\n\", \"3139\\n\", \"32\\n\", \"3601\\n\", \"66\\n\", \"1160764\\n\", \"140\\n\", \"9456\\n\", \"111\\n\", \"136\\n\", \"100\\n\", \"1419244\\n\", \"37\\n\", \"772977\\n\", \"137\\n\", \"343342\\n\", \"9215\\n\", \"768\\n\", \"54744278\\n\", \"755487487\\n\", \"1098\\n\", \"10\\n\"], \"outputs\": [\"20\\n\", \"19\\n\", \"91\\n\", \"9\\n\", \"9\\n\", \"35\\n\", \"24\\n\", \"18\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"22\\n\", \"37\\n\", \"10\\n\", \"53\\n\", \"19\\n\", \"14\\n\", \"17\\n\", \"46\\n\", \"10\\n\", \"15\\n\", \"34\\n\", \"23\\n\", \"35\\n\", \"10\\n\", \"25\\n\", \"18\\n\", \"52\\n\", \"26\\n\", \"56\\n\", \"10\\n\", \"19\\n\", \"10\\n\", \"19\\n\", \"29\\n\", \"18\\n\", \"23\\n\", \"36\\n\", \"36\\n\", \"28\\n\", \"16\\n\", \"33\\n\", \"27\\n\", \"72\\n\", \"11\\n\", \"43\\n\", \"34\\n\", \"32\\n\", \"18\\n\", \"10\\n\", \"13\\n\", \"15\\n\", \"19\\n\", \"11\\n\", \"11\\n\", \"42\\n\", \"15\\n\", \"15\\n\", \"16\\n\", \"18\\n\", \"10\\n\", \"18\\n\", \"35\\n\", \"9\\n\", \"19\\n\", \"64\\n\", \"11\\n\", \"12\\n\", \"33\\n\", \"23\\n\", \"9\\n\", \"16\\n\", \"19\\n\", \"33\\n\", \"46\\n\", \"23\\n\", \"13\\n\", \"13\\n\", \"10\\n\", \"42\\n\", \"15\\n\", \"32\\n\", \"35\\n\", \"44\\n\", \"41\\n\", \"58\\n\", \"18\\n\", \"45\\n\", \"53\\n\", \"16\\n\", \"14\\n\", \"24\\n\", \"15\\n\", \"10\\n\", \"11\\n\", \"26\\n\", \"31\\n\", \"13\\n\", \"16\\n\", \"28\\n\", \"19\\n\", \"13\\n\", \"32\\n\", \"19\\n\", \"37\\n\", \"12\\n\", \"35\\n\", \"33\\n\", \"11\\n\", \"19\\n\", \"52\\n\", \"40\\n\", \"12\\n\", \"29\\n\", \"14\\n\", \"10\\n\", \"38\\n\", \"10\\n\", \"38\\n\", \"16\\n\", \"38\\n\", \"19\\n\", \"32\\n\", \"36\\n\", \"42\\n\", \"12\\n\", \"12\\n\", \"17\\n\", \"28\\n\", \"21\\n\", \"12\\n\", \"13\\n\", \"38\\n\", \"35\\n\", \"45\\n\", \"19\\n\", \"19\\n\", \"10\\n\", \"11\\n\", \"32\\n\", \"35\\n\", \"21\\n\", \"34\\n\", \"26\\n\", \"18\\n\", \"36\\n\", \"19\\n\", \"16\\n\", \"42\\n\", \"11\\n\", \"33\\n\", \"19\\n\", \"13\\n\", \"15\\n\", \"52\\n\", \"37\\n\", \"33\\n\", \"23\\n\", \"18\\n\", \"10\\n\", \"12\\n\", \"19\\n\", \"10\\n\", \"12\\n\", \"15\\n\", \"91\\n\", \"11\\n\", \"26\\n\", \"9\\n\", \"17\\n\", \"53\\n\", \"32\\n\", \"38\\n\", \"14\\n\", \"10\\n\", \"17\\n\", \"15\\n\", \"27\\n\", \"22\\n\", \"37\\n\", \"33\\n\", \"40\\n\", \"35\\n\", \"53\\n\", \"35\\n\", \"11\\n\", \"23\\n\", \"31\\n\", \"16\\n\", \"9\\n\", \"58\\n\", \"12\\n\", \"43\\n\", \"11\\n\", \"18\\n\", \"15\\n\", \"15\\n\", \"18\\n\", \"18\\n\", \"19\\n\", \"18\\n\", \"36\\n\", \"10\\n\", \"10\\n\", \"11\\n\", \"14\\n\", \"44\\n\", \"56\\n\", \"64\\n\", \"28\\n\", \"16\\n\", \"10\\n\", \"19\\n\", \"36\\n\", \"19\\n\", \"38\\n\", \"18\\n\", \"25\\n\", \"15\\n\", \"29\\n\", \"16\\n\", \"33\\n\", \"42\\n\", \"10\\n\", \"19\\n\", \"13\\n\", \"9\\n\", \"32\\n\", \"52\\n\", \"23\\n\", \"16\\n\", \"29\\n\", \"24\\n\", \"46\\n\", \"23\\n\", \"72\\n\", \"32\\n\", \"10\\n\", \"46\\n\", \"10\\n\", \"13\\n\", \"28\\n\", \"35\\n\", \"10\\n\", \"34\\n\", \"9\\n\", \"41\\n\", \"28\\n\", \"10\\n\", \"24\\n\", \"19\\n\", \"12\\n\", \"14\\n\", \"42\\n\", \"10\\n\", \"10\\n\", \"13\\n\", \"16\\n\", \"10\\n\", \"16\\n\", \"33\\n\", \"35\\n\", \"44\\n\", \"22\\n\", \"15\\n\", \"20\\n\", \"18\\n\", \"29\\n\", \"57\\n\", \"30\\n\", \"9\\n\", \"46\\n\", \"14\\n\", \"32\\n\", \"42\\n\", \"13\\n\", \"12\\n\", \"63\\n\", \"40\\n\", \"51\\n\", \"19\\n\", \"11\\n\", \"17\\n\", \"21\\n\", \"28\\n\", \"90\\n\", \"34\\n\", \"49\\n\", \"36\\n\", \"39\\n\", \"24\\n\", \"38\\n\", \"25\\n\", \"26\\n\", \"37\\n\", \"23\\n\", \"54\\n\", \"43\\n\", \"55\\n\", \"52\\n\", \"53\\n\", \"31\\n\", \"45\\n\", \"33\\n\", \"20\\n\", \"18\\n\", \"9\\n\", \"9\\n\", \"15\\n\", \"14\\n\", \"21\\n\", \"16\\n\", \"9\\n\", \"17\\n\", \"19\\n\", \"11\\n\", \"33\\n\", \"12\\n\", \"33\\n\", \"42\\n\", \"34\\n\", \"51\\n\", \"21\\n\", \"42\\n\", \"25\\n\", \"44\\n\", \"9\\n\", \"13\\n\", \"12\\n\", \"19\\n\", \"21\\n\", \"14\\n\", \"11\\n\", \"11\\n\", \"13\\n\", \"19\\n\", \"54\\n\", \"36\\n\", \"42\\n\", \"24\\n\", \"17\\n\", \"30\\n\", \"13\\n\", \"40\\n\", \"24\\n\", \"22\\n\", \"26\\n\", \"19\\n\", \"28\\n\", \"40\\n\", \"12\\n\", \"23\\n\", \"18\\n\", \"39\\n\", \"29\\n\", \"14\\n\", \"37\\n\", \"34\\n\", \"20\\n\", \"19\\n\"]}", "dataset_type": "taco"} |
taco_7412 | deepcoder | Implement the function which should return `true` if given object is a vowel (meaning `a, e, i, o, u`), and `false` otherwise. | {"ground_truth": "{\"fn_name\": \"is_vowel\", \"inputs\": [[\"\"], [\"a\"], [\"E\"], [\"ou\"], [\"z\"], [\"lol\"]], \"outputs\": [[false], [true], [true], [false], [false], [false]]}", "dataset_type": "taco"} |
taco_7413 | deepcoder | Vasya's bicycle chain drive consists of two parts: n stars are attached to the pedal axle, m stars are attached to the rear wheel axle. The chain helps to rotate the rear wheel by transmitting the pedal rotation.
We know that the i-th star on the pedal axle has ai (0 < a1 < a2 < ... < an) teeth, and the j-th star on the rear wheel axle has bj (0 < b1 < b2 < ... < bm) teeth. Any pair (i, j) (1 ≤ i ≤ n; 1 ≤ j ≤ m) is called a gear and sets the indexes of stars to which the chain is currently attached. Gear (i, j) has a gear ratio, equal to the value <image>.
Since Vasya likes integers, he wants to find such gears (i, j), that their ratios are integers. On the other hand, Vasya likes fast driving, so among all "integer" gears (i, j) he wants to choose a gear with the maximum ratio. Help him to find the number of such gears.
In the problem, fraction <image> denotes division in real numbers, that is, no rounding is performed.
Input
The first input line contains integer n (1 ≤ n ≤ 50) — the number of stars on the bicycle's pedal axle. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 104) in the order of strict increasing.
The third input line contains integer m (1 ≤ m ≤ 50) — the number of stars on the rear wheel axle. The fourth line contains m integers b1, b2, ..., bm (1 ≤ bi ≤ 104) in the order of strict increasing.
It is guaranteed that there exists at least one gear (i, j), that its gear ratio is an integer. The numbers on the lines are separated by spaces.
Output
Print the number of "integer" gears with the maximum ratio among all "integer" gears.
Examples
Input
2
4 5
3
12 13 15
Output
2
Input
4
1 2 3 4
5
10 11 12 13 14
Output
1
Note
In the first sample the maximum "integer" gear ratio equals 3. There are two gears that have such gear ratio. For one of them a1 = 4, b1 = 12, and for the other a2 = 5, b3 = 15. | {"ground_truth": "{\"inputs\": [\"1\\n1\\n2\\n1 2\\n\", \"50\\n17 20 22 28 36 38 46 47 48 50 52 57 58 62 63 69 70 74 75 78 79 81 82 86 87 90 93 95 103 202 292 442 1756 1769 2208 2311 2799 2957 3483 4280 4324 4932 5109 5204 6225 6354 6561 7136 8754 9670\\n40\\n68 214 957 1649 1940 2078 2134 2716 3492 3686 4462 4559 4656 4756 4850 5044 5490 5529 5592 5626 6014 6111 6693 6790 7178 7275 7566 7663 7702 7857 7954 8342 8511 8730 8957 9021 9215 9377 9445 9991\\n\", \"3\\n3 4 5\\n3\\n6 20 25\\n\", \"2\\n4 5\\n3\\n12 15 20\\n\", \"50\\n2 4 5 16 18 19 22 23 25 26 34 44 48 54 67 79 80 84 92 110 116 133 138 154 163 171 174 202 205 218 228 229 234 245 247 249 250 263 270 272 274 275 277 283 289 310 312 334 339 342\\n50\\n1 5 17 18 25 37 46 47 48 59 67 75 80 83 84 107 115 122 137 141 159 162 175 180 184 204 221 224 240 243 247 248 249 258 259 260 264 266 269 271 274 293 294 306 329 330 334 335 342 350\\n\", \"39\\n10 13 21 25 36 38 47 48 58 64 68 69 73 79 86 972 2012 2215 2267 2503 3717 3945 4197 4800 5266 6169 6612 6824 7023 7322 7582 7766 8381 8626 8879 9079 9088 9838 9968\\n50\\n432 877 970 1152 1202 1223 1261 1435 1454 1578 1843 1907 2003 2037 2183 2195 2215 2425 3065 3492 3615 3637 3686 3946 4189 4415 4559 4656 4665 4707 4886 4887 5626 5703 5955 6208 6521 6581 6596 6693 6985 7013 7081 7343 7663 8332 8342 8637 9207 9862\\n\", \"20\\n79 113 151 709 809 983 1291 1399 1409 1429 2377 2659 2671 2897 3217 3511 3557 3797 3823 4363\\n10\\n19 101 659 797 1027 1963 2129 2971 3299 9217\\n\", \"50\\n6 9 11 21 28 39 42 56 60 63 81 88 91 95 105 110 117 125 149 165 174 176 185 189 193 196 205 231 233 268 278 279 281 286 289 292 298 303 305 306 334 342 350 353 361 371 372 375 376 378\\n50\\n6 17 20 43 45 52 58 59 82 83 88 102 111 118 121 131 145 173 190 191 200 216 224 225 232 235 243 256 260 271 290 291 321 322 323 329 331 333 334 341 343 348 351 354 356 360 366 379 387 388\\n\", \"20\\n179 359 401 467 521 601 919 941 1103 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taco_7414 | deepcoder | Consider the following process. You have a binary string (a string where each character is either 0 or 1) $w$ of length $n$ and an integer $x$. You build a new binary string $s$ consisting of $n$ characters. The $i$-th character of $s$ is chosen as follows:
if the character $w_{i-x}$ exists and is equal to 1, then $s_i$ is 1 (formally, if $i > x$ and $w_{i-x} = $ 1, then $s_i = $ 1); if the character $w_{i+x}$ exists and is equal to 1, then $s_i$ is 1 (formally, if $i + x \le n$ and $w_{i+x} = $ 1, then $s_i = $ 1); if both of the aforementioned conditions are false, then $s_i$ is 0.
You are given the integer $x$ and the resulting string $s$. Reconstruct the original string $w$.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.
Each test case consists of two lines. The first line contains the resulting string $s$ ($2 \le |s| \le 10^5$, each character of $s$ is either 0 or 1). The second line contains one integer $x$ ($1 \le x \le |s| - 1$).
The total length of all strings $s$ in the input does not exceed $10^5$.
-----Output-----
For each test case, print the answer on a separate line as follows:
if no string $w$ can produce the string $s$ at the end of the process, print $-1$; otherwise, print the binary string $w$ consisting of $|s|$ characters. If there are multiple answers, print any of them.
-----Example-----
Input
3
101110
2
01
1
110
1
Output
111011
10
-1 | {"ground_truth": "{\"inputs\": [\"3\\n101110\\n2\\n01\\n1\\n110\\n1\\n\", \"3\\n100110\\n2\\n01\\n1\\n110\\n1\\n\", \"3\\n100110\\n2\\n01\\n1\\n111\\n1\\n\", \"3\\n100110\\n2\\n01\\n2\\n011\\n1\\n\", \"3\\n000110\\n2\\n01\\n2\\n011\\n1\\n\", \"3\\n001110\\n2\\n01\\n2\\n111\\n1\\n\", \"3\\n001110\\n2\\n01\\n2\\n101\\n1\\n\", \"3\\n100110\\n1\\n01\\n0\\n101\\n1\\n\", \"3\\n100110\\n1\\n01\\n0\\n111\\n1\\n\", \"3\\n101110\\n2\\n01\\n1\\n110\\n2\\n\", \"3\\n100110\\n2\\n01\\n1\\n101\\n1\\n\", \"3\\n100110\\n4\\n01\\n1\\n011\\n1\\n\", \"3\\n100110\\n1\\n01\\n0\\n011\\n1\\n\", \"3\\n100110\\n2\\n01\\n0\\n101\\n1\\n\", \"3\\n100110\\n3\\n01\\n1\\n011\\n1\\n\", \"3\\n000110\\n2\\n1\\n0\\n011\\n1\\n\", \"3\\n100110\\n0\\n01\\n3\\n001\\n1\\n\", \"3\\n111110\\n1\\n01\\n0\\n101\\n1\\n\", \"3\\n101110\\n4\\n01\\n1\\n110\\n0\\n\", \"3\\n001110\\n0\\n01\\n3\\n110\\n1\\n\", \"3\\n111110\\n1\\n1\\n0\\n101\\n1\\n\", \"3\\n101110\\n4\\n01\\n1\\n010\\n0\\n\", \"3\\n100110\\n3\\n1\\n1\\n001\\n1\\n\", 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\"3\\n100110\\n1\\n01\\n3\\n110\\n1\\n\", \"3\\n100110\\n3\\n01\\n1\\n001\\n1\\n\", \"3\\n100100\\n1\\n01\\n2\\n111\\n1\\n\", \"3\\n001110\\n2\\n1\\n0\\n011\\n1\\n\", \"3\\n101100\\n1\\n1\\n6\\n101\\n1\\n\", \"3\\n100110\\n1\\n1\\n1\\n011\\n1\\n\", \"3\\n100110\\n0\\n01\\n3\\n110\\n1\\n\", \"3\\n011110\\n2\\n1\\n0\\n011\\n1\\n\", \"3\\n101100\\n1\\n1\\n1\\n101\\n1\\n\", \"3\\n100110\\n1\\n1\\n1\\n011\\n2\\n\", \"3\\n101110\\n4\\n01\\n0\\n010\\n0\\n\", \"3\\n101110\\n1\\n1\\n1\\n101\\n1\\n\", \"3\\n101111\\n2\\n1\\n1\\n101\\n1\\n\", \"3\\n101111\\n2\\n1\\n2\\n101\\n0\\n\", \"3\\n001111\\n2\\n1\\n2\\n101\\n0\\n\", \"3\\n011101\\n1\\n1\\n0\\n110\\n1\\n\", \"3\\n011101\\n1\\n0\\n0\\n100\\n1\\n\", \"3\\n100100\\n2\\n01\\n1\\n110\\n1\\n\", \"3\\n100110\\n2\\n01\\n1\\n001\\n1\\n\", \"3\\n101110\\n2\\n01\\n1\\n110\\n1\\n\"], \"outputs\": [\"111011\\n10\\n-1\\n\", \"011001\\n10\\n-1\\n\", \"011001\\n10\\n111\\n\", \"011001\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n111\\n\", 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\"011001\\n10\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n010\\n\", \"011001\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n01\\n010\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n111\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n01\\n010\\n\", \"-1\\n10\\n-1\\n\", \"011001\\n-1\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n10\\n-1\\n\", \"-1\\n-1\\n-1\\n\", \"110100\\n10\\n-1\\n\", \"-1\\n-1\\n111\\n\", \"-1\\n1\\n-1\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n-1\\n\", \"100110\\n-1\\n-1\\n\", \"-1\\n1\\n-1\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n-1\\n\", \"-1\\n01\\n010\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n010\\n\", \"-1\\n-1\\n101\\n\", \"-1\\n-1\\n101\\n\", \"-1\\n1\\n-1\\n\", \"-1\\n0\\n-1\\n\", \"-1\\n10\\n-1\\n\", \"011001\\n10\\n-1\\n\", \"111011\\n10\\n-1\\n\"]}", "dataset_type": "taco"} |
taco_7415 | deepcoder | A number is called powerful if it is a power of two or a factorial. In other words, the number $m$ is powerful if there exists a non-negative integer $d$ such that $m=2^d$ or $m=d!$, where $d!=1\cdot 2\cdot \ldots \cdot d$ (in particular, $0! = 1$). For example $1$, $4$, and $6$ are powerful numbers, because $1=1!$, $4=2^2$, and $6=3!$ but $7$, $10$, or $18$ are not.
You are given a positive integer $n$. Find the minimum number $k$ such that $n$ can be represented as the sum of $k$ distinct powerful numbers, or say that there is no such $k$.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.
A test case consists of only one line, containing one integer $n$ ($1\le n\le 10^{12}$).
-----Output-----
For each test case print the answer on a separate line.
If $n$ can not be represented as the sum of distinct powerful numbers, print $-1$.
Otherwise, print a single positive integer — the minimum possible value of $k$.
-----Examples-----
Input
4
7
11
240
17179869184
Output
2
3
4
1
-----Note-----
In the first test case, $7$ can be represented as $7=1+6$, where $1$ and $6$ are powerful numbers. Because $7$ is not a powerful number, we know that the minimum possible value of $k$ in this case is $k=2$.
In the second test case, a possible way to represent $11$ as the sum of three powerful numbers is $11=1+4+6$. We can show that there is no way to represent $11$ as the sum of two or less powerful numbers.
In the third test case, $240$ can be represented as $240=24+32+64+120$. Observe that $240=120+120$ is not a valid representation, because the powerful numbers have to be distinct.
In the fourth test case, $17179869184=2^{34}$, so $17179869184$ is a powerful number and the minimum $k$ in this case is $k=1$. | {"ground_truth": "{\"inputs\": [\"4\\n7\\n11\\n240\\n17179869184\\n\", \"100\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\n\", 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taco_7416 | deepcoder | Theatre Square in the capital city of Berland has a rectangular shape with the size n × m meters. On the occasion of the city's anniversary, a decision was taken to pave the Square with square granite flagstones. Each flagstone is of the size a × a.
What is the least number of flagstones needed to pave the Square? It's allowed to cover the surface larger than the Theatre Square, but the Square has to be covered. It's not allowed to break the flagstones. The sides of flagstones should be parallel to the sides of the Square.
Input
The input contains three positive integer numbers in the first line: n, m and a (1 ≤ n, m, a ≤ 109).
Output
Write the needed number of flagstones.
Examples
Input
6 6 4
Output
4 | {"ground_truth": "{\"inputs\": [\"1 1 3\\n\", \"1000000000 1000000000 1\\n\", \"2 1 2\\n\", \"222 332 5\\n\", \"2 2 1\\n\", \"456784567 1000000000 51\\n\", \"1001 1000 10\\n\", \"2 3 4\\n\", \"1000000000 1000000000 999999999\\n\", \"2 1 1\\n\", \"100 10001 1000000000\\n\", \"39916800 134217728 40320\\n\", \"12 13 4\\n\", \"1000 1000 10\\n\", \"1 1 1\\n\", \"1000000000 987654321 1\\n\", \"1000000000 1000000000 192\\n\", \"1000000000 1000000000 1000000000\\n\", \"1 2 1\\n\", \"1 1 2\\n\", \"222 29 5\\n\", \"343570561 1000000000 51\\n\", \"1011 1000 10\\n\", \"39916800 10156240 40320\\n\", \"12 13 8\\n\", \"1011 1001 10\\n\", \"1000000000 989104164 1\\n\", \"1 3 1\\n\", \"222 29 6\\n\", \"343570561 1000000000 48\\n\", \"39916800 10156240 70333\\n\", \"1000000000 980932347 1\\n\", \"222 29 2\\n\", \"343570561 1000000000 70\\n\", \"39916800 10156240 57294\\n\", \"222 20 2\\n\", \"343570561 1000000000 127\\n\", \"74693241 10156240 57294\\n\", \"196 20 2\\n\", \"134553818 1000000000 127\\n\", \"16584719 10156240 57294\\n\", \"196 34 2\\n\", \"137471975 1000000000 127\\n\", \"14807183 10156240 57294\\n\", \"196 34 4\\n\", \"137471975 1000000000 249\\n\", \"14807183 10831059 57294\\n\", \"191 34 4\\n\", \"113457344 1000000000 249\\n\", \"14807183 10831059 71023\\n\", \"96 34 4\\n\", \"113457344 1000000000 147\\n\", \"14807183 5694465 71023\\n\", \"63170207 1000000000 147\\n\", \"22274484 5694465 71023\\n\", \"22274484 5694465 98159\\n\", \"22274484 5694465 78774\\n\", \"22274484 11362982 78774\\n\", \"22274484 11362982 125506\\n\", \"22274484 16723021 125506\\n\", \"22274484 21105028 125506\\n\", \"34296343 21105028 125506\\n\", \"50098052 21105028 125506\\n\", \"50098052 15419404 125506\\n\", \"50098052 4588018 125506\\n\", \"50098052 4588018 15126\\n\", \"50098052 7072611 15126\\n\", \"50098052 10351641 15126\\n\", \"50098052 12063612 15126\\n\", \"50098052 11818472 15126\\n\", \"50098052 19350434 15126\\n\", \"50098052 19350434 19776\\n\", \"2294471 19350434 19776\\n\", \"4148298 19350434 19776\\n\", \"4148298 19350434 10939\\n\", \"4148298 12193624 10939\\n\", \"4148298 3069329 10939\\n\", \"4148298 2658581 10939\\n\", \"4053251 2658581 10939\\n\", \"4053251 2349138 10939\\n\", \"4053251 2349138 8281\\n\", \"4053251 2349138 9732\\n\", \"4053251 2349138 15424\\n\", \"4053251 2349138 9789\\n\", \"4053251 2349138 18500\\n\", \"4053251 2349138 173\\n\", \"4053251 2349138 222\\n\", \"4053251 2821829 222\\n\", \"4053251 2821829 407\\n\", \"4053251 2169218 407\\n\", \"4963382 2169218 407\\n\", \"4963382 2169218 669\\n\", \"5776484 2169218 669\\n\", \"5776484 2448187 669\\n\", \"8333468 2448187 669\\n\", \"5201780 2448187 669\\n\", \"2731319 2448187 669\\n\", \"2731319 1572672 669\\n\", \"953088 1572672 669\\n\", \"979196 1572672 669\\n\", \"979196 825585 669\\n\", \"979196 825585 832\\n\", \"979196 825585 1439\\n\", \"979196 777876 1439\\n\", \"979196 777876 2326\\n\", \"979196 266369 2326\\n\", \"979010 254319 2326\\n\", \"979010 213559 2326\\n\", \"71066 213559 2326\\n\", \"71066 213559 2635\\n\", \"71066 335845 2635\\n\", \"71066 335845 1269\\n\", \"71066 335845 627\\n\", \"102343 335845 627\\n\", \"50849 335845 627\\n\", \"43093 335845 627\\n\", \"43093 247341 627\\n\", \"43093 247341 713\\n\", \"43093 104798 713\\n\", \"6 6 4\\n\"], \"outputs\": [\"1\\n\", \"1000000000000000000\\n\", \"1\\n\", \"3015\\n\", \"4\\n\", \"175618850864484\\n\", \"10100\\n\", \"1\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"3295710\\n\", \"12\\n\", \"10000\\n\", \"1\\n\", \"987654321000000000\\n\", \"27126743055556\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"270\\n\", \"132091731302232\\n\", \"10200\\n\", \"249480\\n\", \"4\\n\", \"10302\\n\", \"989104164000000000\\n\", \"3\\n\", \"185\\n\", \"149119192271814\\n\", \"82360\\n\", \"980932347000000000\\n\", \"1665\\n\", \"70116446362965\\n\", \"124066\\n\", \"1110\\n\", \"21301425878496\\n\", \"232112\\n\", \"980\\n\", \"8342354597664\\n\", \"51620\\n\", \"1666\\n\", \"8523283737312\\n\", \"46102\\n\", \"441\\n\", \"2217257438305\\n\", \"49210\\n\", \"432\\n\", \"1829928049380\\n\", \"31977\\n\", \"216\\n\", \"5250470091318\\n\", \"16929\\n\", \"2923333725060\\n\", \"25434\\n\", \"13393\\n\", \"20659\\n\", \"41035\\n\", \"16198\\n\", \"23852\\n\", \"30082\\n\", \"46306\\n\", \"67600\\n\", \"49200\\n\", \"14800\\n\", \"1007152\\n\", \"1550484\\n\", \"2269405\\n\", \"2643774\\n\", \"2590766\\n\", \"4240640\\n\", \"2480786\\n\", \"114543\\n\", \"205590\\n\", \"672220\\n\", \"423700\\n\", \"106780\\n\", \"92720\\n\", \"90524\\n\", \"79765\\n\", \"139160\\n\", \"100914\\n\", \"40239\\n\", \"99600\\n\", \"27940\\n\", \"318155970\\n\", \"193206156\\n\", \"232077438\\n\", \"69055706\\n\", \"53081470\\n\", \"65004680\\n\", \"24063060\\n\", \"28003305\\n\", \"31604100\\n\", \"45592620\\n\", \"28460160\\n\", \"14943780\\n\", \"9599133\\n\", \"3350175\\n\", \"3441864\\n\", \"1808040\\n\", \"1168761\\n\", \"390894\\n\", \"368421\\n\", \"141035\\n\", \"48415\\n\", \"46310\\n\", \"38732\\n\", \"2852\\n\", \"2214\\n\", \"3456\\n\", \"15105\\n\", \"61104\\n\", \"87904\\n\", \"43952\\n\", \"36984\\n\", \"27255\\n\", \"21167\\n\", \"8967\\n\", \"4\\n\"]}", "dataset_type": "taco"} |
taco_7417 | deepcoder | You're given an array $b$ of length $n$. Let's define another array $a$, also of length $n$, for which $a_i = 2^{b_i}$ ($1 \leq i \leq n$).
Valerii says that every two non-intersecting subarrays of $a$ have different sums of elements. You want to determine if he is wrong. More formally, you need to determine if there exist four integers $l_1,r_1,l_2,r_2$ that satisfy the following conditions: $1 \leq l_1 \leq r_1 \lt l_2 \leq r_2 \leq n$; $a_{l_1}+a_{l_1+1}+\ldots+a_{r_1-1}+a_{r_1} = a_{l_2}+a_{l_2+1}+\ldots+a_{r_2-1}+a_{r_2}$.
If such four integers exist, you will prove Valerii wrong. Do they exist?
An array $c$ is a subarray of an array $d$ if $c$ can be obtained from $d$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.
The first line of every test case contains a single integer $n$ ($2 \le n \le 1000$).
The second line of every test case contains $n$ integers $b_1,b_2,\ldots,b_n$ ($0 \le b_i \le 10^9$).
-----Output-----
For every test case, if there exist two non-intersecting subarrays in $a$ that have the same sum, output YES on a separate line. Otherwise, output NO on a separate line.
Also, note that each letter can be in any case.
-----Example-----
Input
2
6
4 3 0 1 2 0
2
2 5
Output
YES
NO
-----Note-----
In the first case, $a = [16,8,1,2,4,1]$. Choosing $l_1 = 1$, $r_1 = 1$, $l_2 = 2$ and $r_2 = 6$ works because $16 = (8+1+2+4+1)$.
In the second case, you can verify that there is no way to select to such subarrays. | {"ground_truth": "{\"inputs\": [\"2\\n6\\n4 3 0 1 2 0\\n2\\n2 5\\n\", \"1\\n3\\n1 1 2\\n\", \"1\\n3\\n1 1 1\\n\", \"1\\n3\\n1 2 3\\n\", \"1\\n3\\n1 2 3\\n\", \"1\\n3\\n1 1 1\\n\", \"1\\n3\\n1 1 2\\n\", \"1\\n3\\n1 2 2\\n\", \"2\\n6\\n0 3 0 1 2 0\\n2\\n2 5\\n\", \"1\\n3\\n0 2 1\\n\", \"1\\n3\\n0 1 1\\n\", \"1\\n3\\n0 2 2\\n\", \"1\\n3\\n0 2 4\\n\", \"1\\n3\\n1 2 1\\n\", \"1\\n3\\n1 2 4\\n\", \"1\\n3\\n1 3 1\\n\", \"1\\n3\\n1 0 1\\n\", \"1\\n3\\n2 2 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n4 5\\n\", \"1\\n3\\n2 2 2\\n\", \"1\\n3\\n2 4 2\\n\", \"1\\n3\\n0 1 2\\n\", \"1\\n3\\n0 3 1\\n\", \"1\\n3\\n0 1 4\\n\", \"1\\n2\\n2 2 2\\n\", \"1\\n3\\n1 0 4\\n\", \"1\\n3\\n1 2 0\\n\", \"1\\n3\\n1 0 2\\n\", \"1\\n3\\n0 2 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n4 3\\n\", \"1\\n3\\n2 0 2\\n\", \"1\\n3\\n0 3 2\\n\", \"1\\n3\\n2 1 2\\n\", \"1\\n3\\n0 3 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n4 6\\n\", \"1\\n3\\n3 0 2\\n\", \"1\\n3\\n0 6 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n4 2\\n\", \"1\\n3\\n3 1 2\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n3 2\\n\", \"1\\n3\\n3 1 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n1 2\\n\", \"1\\n3\\n1 1 3\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n1 4\\n\", \"1\\n3\\n2 2 0\\n\", \"2\\n6\\n1 3 0 1 2 0\\n2\\n2 5\\n\", \"1\\n3\\n0 2 0\\n\", \"1\\n3\\n0 0 4\\n\", \"1\\n3\\n1 4 4\\n\", \"1\\n3\\n1 3 0\\n\", \"1\\n3\\n0 0 1\\n\", \"1\\n3\\n2 2 1\\n\", \"2\\n6\\n4 3 0 1 4 0\\n2\\n4 5\\n\", \"1\\n3\\n0 0 2\\n\", \"1\\n3\\n2 8 2\\n\", \"1\\n3\\n-1 1 2\\n\", \"1\\n3\\n0 1 8\\n\", \"1\\n3\\n1 4 0\\n\", \"1\\n3\\n1 -1 2\\n\", \"1\\n3\\n0 4 4\\n\", \"2\\n6\\n5 3 0 1 2 0\\n2\\n4 3\\n\", \"1\\n3\\n4 0 2\\n\", \"1\\n3\\n2 1 4\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n4 9\\n\", \"1\\n3\\n0 6 4\\n\", \"2\\n6\\n4 3 0 2 2 0\\n2\\n3 2\\n\", \"1\\n3\\n3 2 3\\n\", \"2\\n6\\n4 0 0 1 2 0\\n2\\n1 2\\n\", \"1\\n3\\n1 1 0\\n\", \"1\\n3\\n1 3 -1\\n\", \"1\\n3\\n0 4 1\\n\", \"1\\n3\\n1 1 4\\n\", \"1\\n3\\n1 4 1\\n\", \"2\\n6\\n4 4 0 1 4 0\\n2\\n4 5\\n\", \"1\\n3\\n2 1 0\\n\", \"1\\n3\\n-1 1 8\\n\", \"1\\n3\\n0 5 4\\n\", \"2\\n6\\n5 2 0 1 2 0\\n2\\n4 3\\n\", \"1\\n3\\n4 0 0\\n\", \"1\\n3\\n2 1 1\\n\", \"1\\n3\\n0 10 4\\n\", \"2\\n6\\n6 3 0 2 2 0\\n2\\n3 2\\n\", \"1\\n3\\n1 1 -1\\n\", \"1\\n3\\n0 4 2\\n\", \"1\\n3\\n2 4 1\\n\", \"2\\n6\\n4 4 0 1 4 0\\n2\\n0 5\\n\", \"1\\n3\\n0 1 0\\n\", \"2\\n6\\n4 3 0 1 2 0\\n2\\n2 5\\n\"], \"outputs\": [\"YES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\nNO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\nNO\\n\", \"YES\\n\", \"YES\\nNO\\n\"]}", "dataset_type": "taco"} |
taco_7418 | deepcoder | F: Tea Party
Yun decided to hold a tea party at the company.
The shop sells $ N $ sets of bread, each containing $ A_1, A_2, A_3, \ dots, A_N $.
Yun decided to make a sandwich by combining two breads into a pair.
Yun-san is very careful, so I want to make sure that I don't have any leftover bread.
Calculate how many sandwiches you can make at most.
input
The first line is given the integer $ N $.
On the second line, $ N $ integers $ A_1, A_2, A_3, \ dots, A_N $ are given, separated by blanks.
output
Output the maximum number of sandwiches you can make. However, insert a line break at the end.
Constraint
* $ N $ is an integer greater than or equal to $ 1 $ and less than or equal to $ 100 $
* $ A_1, A_2, A_3, \ dots, A_N $ are integers between $ 1 $ and $ 100 $
Input example 1
Five
2 3 5 6 7
Output example 1
Ten
Buy the first, third, fourth, and fifth sets to get $ 20 $ in bread.
If you buy all the sets, you will end up with $ 23 $ of bread and you will have a surplus.
Input example 2
Four
3 5 6 8
Output example 2
11
Example
Input
5
2 3 5 6 7
Output
10 | {"ground_truth": "{\"inputs\": [\"5\\n4 3 5 6 7\", \"5\\n4 3 5 10 7\", \"5\\n4 3 5 10 9\", \"5\\n4 6 5 10 9\", \"5\\n4 12 5 10 9\", \"5\\n4 12 5 0 9\", \"5\\n4 12 5 0 3\", \"5\\n1 12 5 0 3\", \"5\\n2 3 3 6 7\", \"5\\n4 3 5 10 17\", \"5\\n4 6 9 10 9\", \"5\\n6 12 5 0 9\", \"5\\n6 2 5 0 3\", \"5\\n2 12 7 0 0\", \"5\\n4 0 13 10 17\", \"5\\n7 4 11 10 10\", \"5\\n3 3 5 0 44\", \"5\\n0 0 1 10 1\", \"5\\n5 3 5 0 44\", \"5\\n12 21 4 0 9\", \"5\\n9 2 2 0 6\", \"5\\n5 3 5 1 44\", \"5\\n4 0 21 8 17\", \"5\\n4 3 5 1 44\", \"5\\n4 0 35 8 17\", \"5\\n2 33 12 0 1\", \"5\\n4 3 9 1 44\", \"5\\n4 0 35 14 17\", \"5\\n30 21 2 0 15\", \"5\\n0 0 7 6 0\", \"5\\n4 0 35 17 30\", \"5\\n30 21 3 0 15\", \"5\\n4 0 35 23 30\", \"5\\n30 39 3 0 15\", \"5\\n4 0 15 -1 44\", \"5\\n6 0 32 14 30\", \"5\\n6 1 32 22 30\", \"5\\n6 1 32 22 11\", \"5\\n6 1 32 22 15\", \"5\\n7 2 32 22 15\", \"5\\n16 54 4 1 0\", \"5\\n2 1 7 1 83\", \"5\\n20 54 6 1 0\", \"5\\n0 2 3 1 83\", \"5\\n0 0 7 1 0\", \"5\\n50 39 3 0 15\", \"5\\n6 0 50 14 30\", \"5\\n6 1 59 14 30\", \"5\\n1 1 13 1 83\", \"5\\n0 0 6 1 90\", \"5\\n-2 1 1 2 1\", \"5\\n4 0 35 23 58\", \"5\\n50 39 3 1 15\", \"5\\n6 1 59 18 30\", \"5\\n6 1 32 48 30\", \"5\\n6 2 85 22 15\", \"5\\n0 9 2 0 2\", \"5\\n0 0 6 1 120\", \"5\\n0 0 7 0 0\", \"5\\n11 1 59 18 30\", \"5\\n-1 8 3 1 159\", \"5\\n0 0 6 0 162\", \"5\\n7 12 5 0 3\", \"5\\n1 12 5 -1 3\", \"5\\n4 1 5 6 7\", \"5\\n4 4 5 10 7\", \"5\\n4 12 5 10 0\", \"5\\n6 12 5 0 3\", \"5\\n13 12 5 0 3\", \"5\\n1 12 7 0 3\", \"5\\n1 3 3 6 7\", \"5\\n4 1 5 10 7\", \"5\\n7 4 5 10 7\", \"5\\n3 3 5 10 17\", \"5\\n4 0 9 10 9\", \"5\\n4 12 1 10 0\", \"5\\n6 18 5 0 9\", \"5\\n13 12 5 -1 3\", \"5\\n1 12 7 0 0\", \"5\\n1 3 3 6 9\", \"5\\n0 1 5 10 7\", \"5\\n7 4 10 10 7\", \"5\\n3 3 5 0 17\", \"5\\n4 0 9 10 17\", \"5\\n4 5 1 10 0\", \"5\\n6 18 2 0 9\", \"5\\n11 2 5 0 3\", \"5\\n5 12 5 -1 3\", \"5\\n2 3 3 6 9\", \"5\\n0 0 5 10 7\", \"5\\n7 4 10 10 10\", \"5\\n3 3 5 0 32\", \"5\\n5 5 1 10 0\", \"5\\n6 18 4 0 9\", \"5\\n11 2 2 0 3\", \"5\\n5 12 9 -1 3\", \"5\\n2 12 12 0 0\", \"5\\n2 4 3 6 9\", \"5\\n0 0 1 10 7\", \"5\\n4 0 13 5 17\", \"5\\n2 3 5 6 7\"], \"outputs\": [\"11\\n\", \"13\\n\", \"14\\n\", \"17\\n\", \"20\\n\", \"15\\n\", \"12\\n\", \"10\\n\", \"9\\n\", \"18\\n\", \"19\\n\", \"16\\n\", \"8\\n\", \"7\\n\", \"22\\n\", \"21\\n\", \"26\\n\", \"6\\n\", \"27\\n\", \"23\\n\", \"5\\n\", \"29\\n\", \"25\\n\", \"28\\n\", \"32\\n\", \"24\\n\", \"30\\n\", \"35\\n\", \"34\\n\", \"3\\n\", \"43\\n\", \"33\\n\", \"46\\n\", \"42\\n\", \"31\\n\", \"41\\n\", \"45\\n\", \"36\\n\", \"38\\n\", \"39\\n\", \"37\\n\", \"47\\n\", \"40\\n\", \"44\\n\", \"4\\n\", \"52\\n\", \"50\\n\", \"55\\n\", \"49\\n\", \"48\\n\", \"1\\n\", \"60\\n\", \"54\\n\", \"57\\n\", \"58\\n\", \"65\\n\", \"2\\n\", \"63\\n\", \"0\\n\", \"59\\n\", \"85\\n\", \"84\\n\", \"12\\n\", \"10\\n\", \"11\\n\", \"15\\n\", \"13\\n\", \"13\\n\", \"15\\n\", \"11\\n\", \"10\\n\", \"13\\n\", \"14\\n\", \"19\\n\", \"16\\n\", \"13\\n\", \"19\\n\", \"16\\n\", \"10\\n\", \"11\\n\", \"11\\n\", \"19\\n\", \"14\\n\", \"20\\n\", \"10\\n\", \"13\\n\", \"9\\n\", \"12\\n\", \"10\\n\", \"11\\n\", \"17\\n\", \"20\\n\", \"10\\n\", \"14\\n\", \"9\\n\", \"14\\n\", \"13\\n\", \"12\\n\", \"9\\n\", \"17\\n\", \"10\"]}", "dataset_type": "taco"} |
taco_7419 | deepcoder | On the Planet AtCoder, there are four types of bases: A, C, G and T. A bonds with T, and C bonds with G.
You are given a letter b as input, which is A, C, G or T. Write a program that prints the letter representing the base that bonds with the base b.
-----Constraints-----
- b is one of the letters A, C, G and T.
-----Input-----
Input is given from Standard Input in the following format:
b
-----Output-----
Print the letter representing the base that bonds with the base b.
-----Sample Input-----
A
-----Sample Output-----
T | {"ground_truth": "{\"inputs\": [\"A\\n\", \"G\\n\", \"C\\n\", \"T\\n\", \"C\", \"T\", \"C\", \"T\", \"G\", \"A\"], \"outputs\": [\"T\\n\", \"C\\n\", \"G\\n\", \"A\\n\", \"G\\n\", \"A\\n\", \"G\\n\", \"A\\n\", \"C\", \"T\"]}", "dataset_type": "taco"} |
taco_7420 | deepcoder | When Mr. Kay was browsing a certain SNS as usual, the problem that "there are people who can solve IQ150 or more" came to the timeline. Mr. Kay has an IQ of over 150, so he solved the problem in an instant without even looking at it. For him, he doesn't have to work on such a mystery. It is enough to leave it to the computer.
problem
The following mysterious mathematical formula was written in the problem.
* \\ (5 + 3 = 28 \\)
* \\ (9 + 1 = 810 \\)
* \\ (8 + 6 = 214 \\)
* \\ (5 + 4 = 19 \\)
* \\ (2 + 2 = 4 \\)
* \\ (15 + 8 = 723 \\)
* \\ (7 + 9 = -216 \\)
* \\ (3 + 0 = 33 \\)
When thinking about the above operator \\ (+ \\), for a positive integer \\ (a \\) \\ (x \ geq 0, y \ geq 0 \\) and \\ (x + y =) Find the number of integer pairs \\ (x, y \\) such that a \\).
input
A positive integer \\ (a \\) is given on one line.
output
Output the number of pairs \\ ((x, y) \\) that satisfy \\ (a = x + y, x \ geq 0, y \ geq 0 \\) on one line.
Constraint
* \\ (1 \ leq a \ leq 10 ^ 9 (= 1000000000) \\)
Input / output example
Input 1
19
Output 1
1
There is one way of \\ (5 + 4 \\).
Input 2
twenty two
Output 2
2
There are two types: \\ (11 + 11 \\) and \\ (2 + 0 \\).
Input 3
1
Output 3
0
\\ (1 + 0 = 11, 0 + 1 = -11 \\). \\ (1 \\) cannot be generated.
Input 4
101
Output 4
0
Note that \\ (1 --0 \\) is not \\ (101 \\).
Input 5
660233276
Output 5
Four
Example
Input
19
Output
1 | {"ground_truth": "{\"inputs\": [\"5\", \"2\", \"68\", \"2286\", \"7\", \"1\", \"4\", \"27\", \"8\", \"3\", \"49\", \"6\", \"82\", \"75\", \"123\", \"188\", \"13\", \"12\", \"14\", \"24\", \"9\", \"10\", \"15\", \"11\", \"48\", \"18\", \"50\", \"45\", \"31\", \"194\", \"310\", \"30\", \"17\", \"16\", \"28\", \"70\", \"25\", \"80\", \"26\", \"23\", \"294\", \"455\", \"35\", \"114\", \"32\", \"85\", \"51\", \"40\", \"415\", \"411\", \"130\", \"21\", \"62\", \"22\", \"37\", \"772\", \"632\", \"43\", \"38\", \"44\", \"750\", \"441\", \"29\", \"138\", \"20\", \"421\", \"511\", \"90\", \"627\", \"326\", \"74\", \"817\", \"370\", \"39\", \"41\", \"126\", \"53\", \"78\", \"325\", \"314\", \"476\", \"602\", \"420\", \"634\", \"851\", \"746\", \"814\", \"532\", \"1020\", \"1809\", \"2465\", \"4598\", \"4112\", \"2725\", \"3645\", \"2071\", \"76\", \"63\", \"103\", \"101\", \"19\"], \"outputs\": [\"0\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\"]}", "dataset_type": "taco"} |
taco_7421 | deepcoder | You've gotten an n × m sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as A. Set A is connected. Your task is to find the minimum number of squares that we can delete from set A to make it not connected.
A set of painted squares is called connected, if for every two squares a and b from this set there is a sequence of squares from the set, beginning in a and ending in b, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.
Input
The first input line contains two space-separated integers n and m (1 ≤ n, m ≤ 50) — the sizes of the sheet of paper.
Each of the next n lines contains m characters — the description of the sheet of paper: the j-th character of the i-th line equals either "#", if the corresponding square is painted (belongs to set A), or equals "." if the corresponding square is not painted (does not belong to set A). It is guaranteed that the set of all painted squares A is connected and isn't empty.
Output
On the first line print the minimum number of squares that need to be deleted to make set A not connected. If it is impossible, print -1.
Examples
Input
5 4
####
#..#
#..#
#..#
####
Output
2
Input
5 5
#####
#...#
#####
#...#
#####
Output
2
Note
In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.
The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. The deleted squares are marked with crosses.
<image> | {"ground_truth": "{\"inputs\": [\"3 3\\n###\\n#.#\\n###\\n\", \"2 2\\n.#\\n.#\\n\", \"2 2\\n.#\\n##\\n\", \"2 5\\n#####\\n##.##\\n\", \"2 2\\n##\\n#.\\n\", \"5 3\\n###\\n###\\n.#.\\n###\\n###\\n\", \"1 2\\n##\\n\", \"5 7\\n.#####.\\n.#...#.\\n###.###\\n#.#.#.#\\n###.###\\n\", \"5 5\\n#####\\n#####\\n#....\\n#####\\n#####\\n\", \"2 5\\n##.##\\n#####\\n\", \"2 2\\n##\\n..\\n\", \"10 10\\n..........\\n.#####....\\n.#........\\n.#.###....\\n.#.###....\\n.#.###....\\n.#..##....\\n.#####....\\n..........\\n..........\\n\", \"2 2\\n##\\n##\\n\", \"3 5\\n##.##\\n#####\\n##.##\\n\", \"9 9\\n#########\\n#.......#\\n#.#####.#\\n#.#.#.#.#\\n#.#.#.#.#\\n#.#.#.#.#\\n#.#####.#\\n#...#...#\\n#########\\n\", \"20 20\\n.....######.........\\n.....#....#.........\\n.....#....#.........\\n.....#....#.........\\n.....############...\\n.........##.....#...\\n..........#.....#...\\n..........#.....#...\\n..........###...#...\\n............#...#...\\n............#...#...\\n............#...#...\\n............#...#...\\n............#####...\\n....................\\n....................\\n....................\\n....................\\n....................\\n....................\\n\", \"5 5\\n.....\\n.....\\n..#..\\n..#..\\n.....\\n\", \"6 2\\n##\\n##\\n#.\\n##\\n##\\n##\\n\", \"1 50\\n##................................................\\n\", \"3 3\\n...\\n.#.\\n...\\n\", \"4 4\\n####\\n####\\n####\\n####\\n\", \"1 1\\n#\\n\", \"10 10\\n..........\\n..........\\n..........\\n..........\\n...###....\\n...#.#....\\n...#####..\\n.....#.#..\\n.....###..\\n..........\\n\", \"3 3\\n.#.\\n.#.\\n...\\n\", \"5 5\\n###..\\n###..\\n#..##\\n#####\\n#####\\n\", \"7 7\\n##.###.\\n#######\\n#..#..#\\n####.##\\n.....#.\\n######.\\n.##....\\n\", \"3 50\\n....##############################################\\n....#.......#...#..#....#..............#.........#\\n....##############################################\\n\", \"2 1\\n#\\n#\\n\", \"10 10\\n..........\\n..........\\n..........\\n..........\\n###.......\\n#.#.......\\n####......\\n####......\\n####......\\n###.......\\n\", \"50 1\\n#\\n#\\n#\\n#\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n.\\n\", \"5 5\\n#####\\n#####\\n##.##\\n##.##\\n##.##\\n\", \"3 3\\n.#.\\n###\\n.#.\\n\", \"1 10\\n.########.\\n\", \"3 3\\n###\\n##.\\n###\\n\", \"1 50\\n................................................##\\n\", \"2 2\\n#.\\n##\\n\", \"2 2\\n##\\n.#\\n\", \"3 5\\n###.#\\n#####\\n##.##\\n\", \"5 5\\n###..\\n..###\\n#..##\\n#####\\n#####\\n\", \"5 1\\n#####\\n#####\\n#....\\n#####\\n#####\\n\", \"5 1\\n###..\\n###..\\n#..##\\n#####\\n#####\\n\", \"2 5\\n#.###\\n#####\\n\", \"10 10\\n..........\\n.#####....\\n.#........\\n.#.###....\\n.#.###....\\n##.##.....\\n.#..##....\\n.#####....\\n..........\\n..........\\n\", \"7 7\\n##.###.\\n#######\\n#..#..#\\n####.##\\n.....#.\\n######.\\n....##.\\n\", \"3 2\\n...\\n.#.\\n...\\n\", \"3 3\\n.#.\\n###\\n#..\\n\", \"5 1\\n###..\\n###/.\\n#..##\\n#####\\n#####\\n\", \"3 2\\n...\\n.#-\\n...\\n\", \"5 1\\n###..\\n###/.\\n#..#\\\"\\n#####\\n#####\\n\", \"5 1\\n###..\\n###/.\\n#..#\\\"\\n####$\\n#####\\n\", \"10 10\\n..........\\n..........\\n..........\\n..........\\n....###...\\n...#.#....\\n...#####..\\n.....#.#..\\n.....###..\\n..........\\n\", \"5 5\\n###..\\n###..\\n##..#\\n#####\\n#####\\n\", \"1 5\\n.########.\\n\", \"5 5\\n#####\\n#...#\\n#####\\n#...#\\n#####\\n\", \"5 4\\n####\\n#..#\\n#..#\\n#..#\\n####\\n\"], \"outputs\": [\"2\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"-1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\"]}", "dataset_type": "taco"} |
taco_7422 | deepcoder | Takahashi has A cookies, and Aoki has B cookies.
Takahashi will do the following action K times:
- If Takahashi has one or more cookies, eat one of his cookies.
- Otherwise, if Aoki has one or more cookies, eat one of Aoki's cookies.
- If they both have no cookies, do nothing.
In the end, how many cookies will Takahashi and Aoki have, respectively?
-----Constraints-----
- 0 \leq A \leq 10^{12}
- 0 \leq B \leq 10^{12}
- 0 \leq K \leq 10^{12}
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
A B K
-----Output-----
Print the numbers of Takahashi's and Aoki's cookies after K actions.
-----Sample Input-----
2 3 3
-----Sample Output-----
0 2
Takahashi will do the following:
- He has two cookies, so he eats one of them.
- Now he has one cookie left, and he eats it.
- Now he has no cookies left, but Aoki has three, so Takahashi eats one of them.
Thus, in the end, Takahashi will have 0 cookies, and Aoki will have 2. | {"ground_truth": "{\"inputs\": [\"2 3 3\\n\", \"500000000000 500000000000 1000000000000\\n\", \"500000000000 500000000001 1000000000000\\n\", \"500000000000 499999999999 1000000000000\\n\", \"0 0 0\\n\", \"0 0 1000000000000\\n\", \"0 1000000000000 0\\n\", \"0 1000000000000 1000000000000\\n\", \"1000000000000 0 0\\n\", \"1000000000000 0 1000000000000\\n\", \"1000000000000 1000000000000 0\\n\", \"1000000000000 1000000000000 1000000000000\\n\", \"999664720736 99150401673 9177110689\\n\", \"999553244087 9473760141 99451169880\\n\", \"99818575601 999284522381 9657141929\\n\", \"99374288514 9551434405 999519154734\\n\", \"9352360840 999532174388 99550343731\\n\", \"9839285289 99663130322 999454076321\\n\", \"500000000000 274588616851 1000000000000\", \"2 3 1\", \"2 3 2\", \"2 3 0\", \"2 6 0\", \"4 6 0\", \"8 6 0\", \"10 6 0\", \"498881727339 49011419508 0000000100000\", \"0 6 0\", \"498881727339 49011419508 0000001100000\", \"0 9 0\", \"498881727339 50858735181 0000001100000\", \"498881727339 64133142411 0000001100000\", \"498881727339 86551688904 0000001100000\", \"498881727339 86551688904 0000000100000\", \"498881727339 88952939337 0000000100000\", \"498881727339 88952939337 0000010100000\", \"623031139973 88952939337 0000010100000\", \"623031139973 53371298929 0000010100000\", \"488984103352 53371298929 0000010100000\", \"488984103352 28853843669 0000010100000\", \"488984103352 44514766879 0000010100000\", \"488984103352 24648370780 0000010100000\", \"488984103352 11555398095 0000010100000\", \"551061056476 11555398095 0000010100000\", \"551061056476 2744039490 0000010100000\", \"551061056476 2744039490 0000010100100\", \"551061056476 2744039490 0010010100100\", \"690068676694 2744039490 0010010100100\", \"810189303696 2744039490 0010010100100\", \"810189303696 304656088 0010010100100\", \"810189303696 304656088 0010010101100\", \"810189303696 559952381 0010010101100\", \"878339967763 559952381 0010010101100\", \"878339967763 559952381 0010010101101\", \"1138880556104 559952381 0010010101101\", \"1138880556104 516416634 0010010101101\", \"637172716773 516416634 0010010101101\", \"1127076073437 516416634 0010010101101\", \"1127076073437 516416634 0010010100101\", \"1127076073437 516416634 0010010100001\", \"1485644197907 516416634 0010010100001\", \"40795666163 516416634 0010010100001\", \"40795666163 581054487 0010010100001\", \"40795666163 581054487 0010010110001\", \"22565061889 581054487 0010010110001\", \"22565061889 581054487 0010110110001\", \"18064166595 581054487 0010110110001\", \"9875757521 933260677 0010110110000\", \"1547869 73650225 0000000111100\", \"204065 73650225 0000000111100\", \"362104 73650225 0000000111100\", \"362104 24404642 0000000111100\", \"362104 16911655 0000000111100\", \"283244830608 274588616851 1000000000000\", \"498881727339 274588616851 1000000000000\", \"498881727339 92988479429 1000000000000\", \"498881727339 92988479429 1010000000000\", \"498881727339 92988479429 1000000100000\", \"498881727339 49011419508 1000000100000\", \"0 0 0\", \"-1 0 0\", \"-1 0 1\", \"-2 0 1\", \"0 0 1\", \"0 -1 1\", \"0 -1 2\", \"4188594464 581054487 0010110110001\", \"7578113331 581054487 0010110110001\", \"7578113331 581054487 0010110110000\", \"7578113331 933260677 0010110110000\", \"9875757521 933260677 1010110110000\", \"9875757521 933260677 1010110100000\", \"9875757521 933260677 1110110100000\", \"9875757521 933260677 1110110100001\", \"8901212864 933260677 1110110100001\", \"8901212864 933260677 1110010100001\", \"9957043226 933260677 1110010100001\", \"9957043226 933260677 1110110100001\", \"13071060683 933260677 1110110100001\", \"13071060683 933260677 1010110100001\", \"24844196728 933260677 1010110100001\", \"24844196728 933260677 1010010100001\", \"46282745761 933260677 1010010100001\", \"46282745761 933260677 1010010100011\", \"46282745761 1063903834 1010010100011\", \"46282745761 1953749145 1010010100011\", \"46282745761 3894888655 1010010100011\", \"82916368507 3894888655 1010010100011\", \"125508515642 3894888655 1010010100011\", \"250272688906 3894888655 1010010100011\", \"250272688906 5812721198 1010010100011\", \"250272688906 9468746842 1010010100011\", \"143395449423 9468746842 1010010100011\", \"223869749260 9468746842 1010010100011\", \"223869749260 13514692621 1010010100011\", \"223869749260 13514692621 1010010101011\", \"223869749260 13514692621 1011010101011\", \"223869749260 13514692621 1011010101111\", \"500000000000 500000000000 1000000000000\", \"2 3 3\"], \"outputs\": [\"0 2\\n\", \"0 0\\n\", \"0 1\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 1000000000000\\n\", \"0 0\\n\", \"1000000000000 0\\n\", \"0 0\\n\", \"1000000000000 1000000000000\\n\", \"0 1000000000000\\n\", \"990487610047 99150401673\\n\", \"900102074207 9473760141\\n\", \"90161433672 999284522381\\n\", \"0 0\\n\", \"0 909334191497\\n\", \"0 0\\n\", \"0 0\\n\", \"1 3\\n\", \"0 3\\n\", \"2 3\\n\", \"2 6\\n\", \"4 6\\n\", \"8 6\\n\", \"10 6\\n\", \"498881627339 49011419508\\n\", \"0 6\\n\", \"498880627339 49011419508\\n\", \"0 9\\n\", \"498880627339 50858735181\\n\", \"498880627339 64133142411\\n\", \"498880627339 86551688904\\n\", \"498881627339 86551688904\\n\", \"498881627339 88952939337\\n\", \"498871627339 88952939337\\n\", \"623021039973 88952939337\\n\", \"623021039973 53371298929\\n\", \"488974003352 53371298929\\n\", \"488974003352 28853843669\\n\", \"488974003352 44514766879\\n\", \"488974003352 24648370780\\n\", \"488974003352 11555398095\\n\", \"551050956476 11555398095\\n\", \"551050956476 2744039490\\n\", \"551050956376 2744039490\\n\", \"541050956376 2744039490\\n\", \"680058576594 2744039490\\n\", \"800179203596 2744039490\\n\", \"800179203596 304656088\\n\", \"800179202596 304656088\\n\", \"800179202596 559952381\\n\", \"868329866663 559952381\\n\", \"868329866662 559952381\\n\", \"1128870455003 559952381\\n\", \"1128870455003 516416634\\n\", \"627162615672 516416634\\n\", \"1117065972336 516416634\\n\", \"1117065973336 516416634\\n\", \"1117065973436 516416634\\n\", \"1475634097906 516416634\\n\", \"30785566162 516416634\\n\", \"30785566162 581054487\\n\", \"30785556162 581054487\\n\", \"12554951888 581054487\\n\", \"12454951888 581054487\\n\", \"7954056594 581054487\\n\", \"0 698908198\\n\", \"1436769 73650225\\n\", \"92965 73650225\\n\", \"251004 73650225\\n\", \"251004 24404642\\n\", \"251004 16911655\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\\n\", \"0 0\", \"0 2\"]}", "dataset_type": "taco"} |
taco_7423 | deepcoder | Write a program which prints $n$-th fibonacci number for a given integer $n$. The $n$-th fibonacci number is defined by the following recursive formula:
\begin{equation*} fib(n)= \left \\{ \begin{array}{ll} 1 & (n = 0) \\\ 1 & (n = 1) \\\ fib(n - 1) + fib(n - 2) & \\\ \end{array} \right. \end{equation*}
Constraints
* $0 \leq n \leq 44$
Input
An integer $n$ is given.
Example
Input
3
Output
3 | {"ground_truth": "{\"inputs\": [\"1\", \"2\", \"4\", \"8\", \"6\", \"15\", \"7\", \"24\", \"14\", \"5\", \"13\", \"11\", \"22\", \"9\", \"29\", \"12\", \"10\", \"41\", \"16\", \"30\", \"21\", \"28\", \"17\", \"34\", \"18\", \"38\", \"31\", \"44\", \"36\", \"32\", \"33\", \"23\", \"19\", \"27\", \"20\", \"37\", \"25\", \"26\", \"42\", \"43\", \"35\", \"39\", \"40\", \"001\", \"6\", \"12\", \"17\", \"24\", \"31\", \"5\", \"2\", \"4\", \"15\", \"30\", \"8\", \"1\", \"10\", \"11\", \"16\", \"9\", \"7\", \"13\", \"27\", \"25\", \"14\", \"19\", \"44\", \"22\", \"23\", \"43\", \"21\", \"36\", \"20\", \"18\", \"29\", \"38\", \"32\", \"35\", \"33\", \"40\", \"28\", \"41\", \"26\", \"34\", \"39\", \"42\", \"37\", \"001\", \"3\"], \"outputs\": [\"1\\n\", \"2\\n\", \"5\\n\", \"34\\n\", \"13\\n\", \"987\\n\", \"21\\n\", \"75025\\n\", \"610\\n\", \"8\\n\", \"377\\n\", \"144\\n\", \"28657\\n\", \"55\\n\", \"832040\\n\", \"233\\n\", \"89\\n\", \"267914296\\n\", \"1597\\n\", \"1346269\\n\", \"17711\\n\", \"514229\\n\", \"2584\\n\", \"9227465\\n\", \"4181\\n\", \"63245986\\n\", \"2178309\\n\", \"1134903170\\n\", \"24157817\\n\", \"3524578\\n\", \"5702887\\n\", \"46368\\n\", \"6765\\n\", \"317811\\n\", \"10946\\n\", \"39088169\\n\", \"121393\\n\", \"196418\\n\", \"433494437\\n\", \"701408733\\n\", \"14930352\\n\", \"102334155\\n\", \"165580141\\n\", \"1\\n\", \"13\\n\", \"233\\n\", \"2584\\n\", \"75025\\n\", \"2178309\\n\", \"8\\n\", \"2\\n\", \"5\\n\", \"987\\n\", \"1346269\\n\", \"34\\n\", \"1\\n\", \"89\\n\", \"144\\n\", \"1597\\n\", \"55\\n\", \"21\\n\", \"377\\n\", \"317811\\n\", \"121393\\n\", \"610\\n\", \"6765\\n\", \"1134903170\\n\", \"28657\\n\", \"46368\\n\", \"701408733\\n\", \"17711\\n\", \"24157817\\n\", \"10946\\n\", \"4181\\n\", \"832040\\n\", \"63245986\\n\", \"3524578\\n\", \"14930352\\n\", \"5702887\\n\", \"165580141\\n\", \"514229\\n\", \"267914296\\n\", \"196418\\n\", \"9227465\\n\", \"102334155\\n\", \"433494437\\n\", \"39088169\\n\", \"1\\n\", \"3\"]}", "dataset_type": "taco"} |
taco_7424 | deepcoder | # Task
You are given a decimal number `n` as a **string**. Transform it into an array of numbers (given as **strings** again), such that each number has only one nonzero digit and their sum equals n.
Each number in the output array should be written without any leading and trailing zeros.
# Input/Output
- `[input]` string `n`
A non-negative number.
`1 ≤ n.length ≤ 30.`
- `[output]` a string array
Elements in the array should be sorted in descending order.
# Example
For `n = "7970521.5544"` the output should be:
```
["7000000",
"900000",
"70000",
"500",
"20",
"1",
".5",
".05",
".004",
".0004"]
```
For `n = "7496314"`, the output should be:
```
["7000000",
"400000",
"90000",
"6000",
"300",
"10",
"4"]
```
For `n = "0"`, the output should be `[]` | {"ground_truth": "{\"fn_name\": \"split_exp\", \"inputs\": [[\"7970521.5544\"], [\"7496314\"], [\"0\"], [\"6\"], [\"1.0000000000\"], [\"0000000000.1\"], [\"1010101\"], [\"1234567890.1234567890\"]], \"outputs\": [[[\"7000000\", \"900000\", \"70000\", \"500\", \"20\", \"1\", \".5\", \".05\", \".004\", \".0004\"]], [[\"7000000\", \"400000\", \"90000\", \"6000\", \"300\", \"10\", \"4\"]], [[]], [[\"6\"]], [[\"1\"]], [[\".1\"]], [[\"1000000\", \"10000\", \"100\", \"1\"]], [[\"1000000000\", \"200000000\", \"30000000\", \"4000000\", \"500000\", \"60000\", \"7000\", \"800\", \"90\", \".1\", \".02\", \".003\", \".0004\", \".00005\", \".000006\", \".0000007\", \".00000008\", \".000000009\"]]]}", "dataset_type": "taco"} |
taco_7425 | deepcoder | Everlasting Sa-Ga, a new, hot and very popular role-playing game, is out on October 19, 2008. Fans have been looking forward to a new title of Everlasting Sa-Ga.
Little Jimmy is in trouble. He is a seven-year-old boy, and he obtained the Everlasting Sa-Ga and is attempting to reach the end of the game before his friends. However, he is facing difficulty solving the riddle of the first maze in this game -- Everlasting Sa-Ga is notorious in extremely hard riddles like Neverending Fantasy and Forever Quest.
The riddle is as follows. There are two doors on the last floor of the maze: the door to the treasure repository and the gate to the hell. If he wrongly opens the door to the hell, the game is over and his save data will be deleted. Therefore, he should never open the wrong door.
So now, how can he find the door to the next stage? There is a positive integer given for each door -- it is a great hint to this riddle. The door to the treasure repository has the integer that gives the larger key number. The key number of a positive integer n is the largest prime factor minus the total sum of any other prime factors, where the prime factors are the prime numbers that divide into n without leaving a remainder. Note that each prime factor should be counted only once.
As an example, suppose there are doors with integers 30 and 20 respectively. Since 30 has three prime factors 2, 3 and 5, its key number is 5 - (2 + 3) = 0. Similarly, since 20 has two prime factors 2 and 5, its key number 20 is 5 - 2 = 3. Jimmy therefore should open the door with 20.
Your job is to write a program to help Jimmy by solving this riddle.
Input
The input is a sequence of datasets. Each dataset consists of a line that contains two integers a and b separated by a space (2 ≤ a, b ≤ 106 ). It is guaranteed that key numbers of these integers are always different.
The input is terminated by a line with two zeros. This line is not part of any datasets and thus should not be processed.
Output
For each dataset, print in a line ‘a’ (without quotes) if the door with the integer a is connected to the treasure repository; print ‘b’ otherwise. No extra space or character is allowed.
Example
Input
10 15
30 20
0 0
Output
a
b | {"ground_truth": "{\"inputs\": [\"10 3\\n30 20\\n0 0\", \"9 15\\n30 20\\n0 0\", \"10 3\\n44 33\\n0 0\", \"10 4\\n11 70\\n0 0\", \"10 3\\n8 20\\n0 0\", \"4 3\\n8 20\\n0 0\", \"4 3\\n12 20\\n0 0\", \"10 3\\n30 33\\n0 0\", \"10 3\\n8 35\\n0 0\", \"8 3\\n8 20\\n0 0\", \"4 5\\n12 20\\n0 0\", \"9 15\\n30 3\\n0 0\", \"2 3\\n44 33\\n0 0\", \"2 3\\n15 33\\n0 0\", \"2 3\\n15 11\\n0 0\", \"10 24\\n30 20\\n0 0\", \"10 3\\n4 20\\n0 0\", \"10 5\\n8 20\\n0 0\", \"4 3\\n6 20\\n0 0\", \"10 3\\n11 35\\n0 0\", \"6 3\\n8 20\\n0 0\", \"9 27\\n30 3\\n0 0\", \"2 3\\n29 33\\n0 0\", \"2 3\\n15 47\\n0 0\", \"2 3\\n15 16\\n0 0\", \"19 24\\n30 20\\n0 0\", \"10 3\\n11 70\\n0 0\", \"6 6\\n8 20\\n0 0\", \"9 30\\n30 3\\n0 0\", \"2 3\\n39 33\\n0 0\", \"9 30\\n30 6\\n0 0\", \"2 3\\n39 38\\n0 0\", \"10 6\\n11 70\\n0 0\", \"9 30\\n7 6\\n0 0\", \"4 3\\n39 38\\n0 0\", \"10 3\\n11 106\\n0 0\", \"10 3\\n11 150\\n0 0\", \"5 3\\n11 150\\n0 0\", \"2 3\\n11 150\\n0 0\", \"2 3\\n11 77\\n0 0\", \"10 15\\n58 20\\n0 0\", \"18 3\\n30 20\\n0 0\", \"10 3\\n16 20\\n0 0\", \"4 6\\n8 20\\n0 0\", \"4 3\\n23 20\\n0 0\", \"9 15\\n30 10\\n0 0\", \"10 2\\n30 33\\n0 0\", \"5 5\\n12 20\\n0 0\", \"8 15\\n30 3\\n0 0\", \"4 3\\n44 33\\n0 0\", \"2 4\\n44 33\\n0 0\", \"2 3\\n15 65\\n0 0\", \"2 2\\n15 11\\n0 0\", \"11 24\\n30 20\\n0 0\", \"10 5\\n2 20\\n0 0\", \"6 3\\n8 26\\n0 0\", \"2 3\\n10 33\\n0 0\", \"2 3\\n15 88\\n0 0\", \"2 3\\n15 28\\n0 0\", \"19 24\\n30 3\\n0 0\", \"10 5\\n11 70\\n0 0\", \"6 6\\n8 33\\n0 0\", \"9 14\\n30 3\\n0 0\", \"18 30\\n30 6\\n0 0\", \"2 3\\n39 71\\n0 0\", \"4 3\\n11 106\\n0 0\", \"2 3\\n11 107\\n0 0\", \"2 3\\n15 77\\n0 0\", \"10 5\\n58 20\\n0 0\", \"18 5\\n30 20\\n0 0\", \"10 5\\n16 20\\n0 0\", \"4 3\\n23 8\\n0 0\", \"9 15\\n29 10\\n0 0\", \"5 5\\n6 20\\n0 0\", \"8 15\\n52 3\\n0 0\", \"10 5\\n3 20\\n0 0\", \"19 24\\n57 3\\n0 0\", \"10 5\\n11 50\\n0 0\", \"6 6\\n11 33\\n0 0\", \"18 30\\n30 4\\n0 0\", \"6 5\\n16 20\\n0 0\", \"9 15\\n29 4\\n0 0\", \"10 5\\n3 35\\n0 0\", \"6 5\\n32 20\\n0 0\", \"10 15\\n29 4\\n0 0\", \"11 5\\n32 20\\n0 0\", \"11 5\\n43 20\\n0 0\", \"10 15\\n30 22\\n0 0\", \"10 3\\n30 21\\n0 0\", \"8 3\\n12 20\\n0 0\", \"9 15\\n30 39\\n0 0\", \"9 15\\n30 4\\n0 0\", \"2 3\\n81 33\\n0 0\", \"2 3\\n15 13\\n0 0\", \"2 5\\n8 20\\n0 0\", \"4 3\\n3 20\\n0 0\", \"10 3\\n7 35\\n0 0\", \"6 3\\n14 20\\n0 0\", \"2 3\\n27 47\\n0 0\", \"2 6\\n15 16\\n0 0\", \"10 15\\n30 20\\n0 0\"], \"outputs\": [\"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"a\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"a\\na\\n\", \"a\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"a\\na\\n\", \"b\\na\\n\", \"b\\na\\n\", \"a\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"a\\nb\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"a\\na\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"a\\na\\n\", \"b\\na\\n\", \"b\\na\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"a\\na\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"a\\na\\n\", \"a\\nb\\n\", \"a\\na\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"a\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\nb\\n\", \"b\\na\\n\", \"b\\na\\n\", \"b\\nb\\n\", \"a\\nb\\n\", \"a\\nb\"]}", "dataset_type": "taco"} |
taco_7426 | deepcoder | Tanechka is shopping in the toy shop. There are exactly $n$ toys in the shop for sale, the cost of the $i$-th toy is $i$ burles. She wants to choose two toys in such a way that their total cost is $k$ burles. How many ways to do that does she have?
Each toy appears in the shop exactly once. Pairs $(a, b)$ and $(b, a)$ are considered equal. Pairs $(a, b)$, where $a=b$, are not allowed.
-----Input-----
The first line of the input contains two integers $n$, $k$ ($1 \le n, k \le 10^{14}$) — the number of toys and the expected total cost of the pair of toys.
-----Output-----
Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is $k$ burles.
-----Examples-----
Input
8 5
Output
2
Input
8 15
Output
1
Input
7 20
Output
0
Input
1000000000000 1000000000001
Output
500000000000
-----Note-----
In the first example Tanechka can choose the pair of toys ($1, 4$) or the pair of toys ($2, 3$).
In the second example Tanechka can choose only the pair of toys ($7, 8$).
In the third example choosing any pair of toys will lead to the total cost less than $20$. So the answer is 0.
In the fourth example she can choose the following pairs: $(1, 1000000000000)$, $(2, 999999999999)$, $(3, 999999999998)$, ..., $(500000000000, 500000000001)$. 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taco_7427 | deepcoder | There are N integers written on a blackboard. The i-th integer is A_i, and the greatest common divisor of these integers is 1.
Takahashi and Aoki will play a game using these integers. In this game, starting from Takahashi the two player alternately perform the following operation:
* Select one integer on the blackboard that is not less than 2, and subtract 1 from the integer.
* Then, divide all the integers on the black board by g, where g is the greatest common divisor of the integers written on the blackboard.
The player who is left with only 1s on the blackboard and thus cannot perform the operation, loses the game. Assuming that both players play optimally, determine the winner of the game.
Constraints
* 1 ≦ N ≦ 10^5
* 1 ≦ A_i ≦ 10^9
* The greatest common divisor of the integers from A_1 through A_N is 1.
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 … A_N
Output
If Takahashi will win, print `First`. If Aoki will win, print `Second`.
Examples
Input
3
3 6 7
Output
First
Input
4
1 2 4 8
Output
First
Input
5
7 8 8 8 8
Output
Second | {"ground_truth": "{\"inputs\": [\"3\\n3 9 7\", \"4\\n1 2 1 9\", \"4\\n1 2 1 8\", \"5\\n7 2 8 8 8\", \"3\\n3 9 9\", \"3\\n3 1 9\", \"4\\n1 2 1 13\", \"3\\n1 1 9\", \"4\\n1 2 1 22\", \"3\\n0 1 9\", \"4\\n1 1 1 22\", \"3\\n0 1 5\", \"4\\n0 1 1 22\", \"4\\n0 0 1 22\", \"4\\n0 -1 1 22\", \"4\\n0 0 1 1\", \"4\\n0 0 1 2\", \"4\\n1 0 1 2\", \"4\\n1 1 1 2\", \"4\\n1 1 1 4\", \"4\\n2 1 1 4\", \"4\\n2 1 1 1\", \"4\\n2 0 1 1\", \"4\\n2 0 0 1\", \"4\\n2 1 0 1\", \"4\\n2 1 0 0\", \"4\\n2 1 0 -1\", \"4\\n2 1 -1 0\", \"3\\n3 6 4\", \"5\\n7 8 4 8 8\", \"3\\n3 4 7\", \"4\\n1 2 1 5\", \"5\\n7 2 8 8 2\", \"3\\n3 9 2\", \"4\\n1 2 1 11\", \"3\\n3 1 3\", \"4\\n1 1 1 13\", \"3\\n1 2 9\", \"4\\n2 2 1 22\", \"3\\n0 1 15\", \"4\\n1 0 1 22\", \"4\\n-1 0 1 22\", \"4\\n0 -1 2 22\", \"4\\n0 1 1 1\", \"4\\n0 -1 1 2\", \"4\\n1 0 0 2\", \"4\\n1 1 2 2\", \"4\\n1 0 1 4\", \"4\\n3 1 1 4\", \"4\\n-1 1 1 1\", \"4\\n1 1 1 1\", \"4\\n0 0 0 1\", \"4\\n2 1 0 2\", \"4\\n4 1 0 0\", \"4\\n2 1 1 -1\", \"4\\n2 2 -1 0\", \"3\\n2 6 4\", \"5\\n7 8 4 8 11\", \"4\\n1 2 0 5\", \"5\\n7 2 8 12 2\", \"3\\n5 9 2\", \"4\\n1 2 0 11\", \"3\\n5 1 3\", \"4\\n1 1 1 14\", \"3\\n1 4 9\", \"4\\n1 2 1 19\", \"4\\n-1 0 1 33\", \"4\\n-1 0 1 23\", \"4\\n1 -1 2 22\", \"4\\n-1 1 1 2\", \"4\\n-1 -1 1 2\", \"4\\n1 -1 0 2\", \"4\\n1 1 2 4\", \"4\\n1 0 0 4\", \"4\\n2 1 1 8\", \"4\\n-1 1 0 1\", \"4\\n0 2 1 1\", \"4\\n0 -1 0 1\", \"4\\n0 1 0 2\", \"4\\n3 1 0 0\", \"4\\n2 0 -1 0\", \"3\\n4 6 4\", \"5\\n7 8 4 5 11\", \"4\\n1 2 -1 5\", \"5\\n7 2 10 12 2\", \"3\\n5 10 2\", \"3\\n5 2 3\", \"4\\n1 1 1 3\", \"3\\n1 0 9\", \"4\\n1 0 1 19\", \"4\\n-1 1 1 33\", \"4\\n-1 0 1 28\", \"4\\n0 -1 2 3\", \"4\\n-1 1 2 2\", \"4\\n-1 -1 1 0\", \"4\\n1 -1 1 2\", \"4\\n2 1 2 4\", \"4\\n1 -1 0 4\", \"4\\n2 1 1 15\", \"4\\n-1 2 0 1\", \"3\\n3 6 7\", \"4\\n1 2 4 8\", \"5\\n7 8 8 8 8\"], \"outputs\": [\"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\", \"First\", \"Second\"]}", "dataset_type": "taco"} |
taco_7428 | deepcoder | In this Kata, you will be given a number `n` (`n > 0`) and your task will be to return the smallest square number `N` (`N > 0`) such that `n + N` is also a perfect square. If there is no answer, return `-1` (`nil` in Clojure, `Nothing` in Haskell, `None` in Rust).
```clojure
solve 13 = 36
; because 36 is the smallest perfect square that can be added to 13 to form a perfect square => 13 + 36 = 49
solve 3 = 1 ; 3 + 1 = 4, a perfect square
solve 12 = 4 ; 12 + 4 = 16, a perfect square
solve 9 = 16
solve 4 = nil
```
```csharp
solve(13) = 36
//because 36 is the smallest perfect square that can be added to 13 to form a perfect square => 13 + 36 = 49
solve(3) = 1 // 3 + 1 = 4, a perfect square
solve(12) = 4 // 12 + 4 = 16, a perfect square
solve(9) = 16
solve(4) = -1
```
```haskell
solve 13 = Just 36
-- because 36 is the smallest perfect square that can be added to 13 to form a perfect square => 13 + 36 = 49
solve 3 = Just 1 -- 3 + 1 = 4, a perfect square
solve 12 = Just 4 -- 12 + 4 = 16, a perfect square
solve 9 = Just 16
solve 4 = Nothing
```
```python
solve(13) = 36
# because 36 is the smallest perfect square that can be added to 13 to form a perfect square => 13 + 36 = 49
solve(3) = 1 # 3 + 1 = 4, a perfect square
solve(12) = 4 # 12 + 4 = 16, a perfect square
solve(9) = 16
solve(4) = -1
```
More examples in test cases.
Good luck! | {"ground_truth": "{\"fn_name\": \"solve\", \"inputs\": [[1], [2], [3], [4], [5], [7], [8], [9], [10], [11], [13], [17], [88901], [290101]], \"outputs\": [[-1], [-1], [1], [-1], [4], [9], [1], [16], [-1], [25], [36], [64], [5428900], [429235524]]}", "dataset_type": "taco"} |
taco_7429 | deepcoder | A game is played on a strip consisting of N cells consecutively numbered from 1 to N.
Alice has her token on cell A. Borys has his token on a different cell B.
Players take turns, Alice moves first. The moving player must shift his or her token from its current cell X to the neighboring cell on the left, cell X-1, or on the right, cell X+1. Note that it's disallowed to move the token outside the strip or to the cell with the other player's token. In one turn, the token of the moving player must be shifted exactly once.
The player who can't make a move loses, and the other player wins.
Both players want to win. Who wins if they play optimally?
Constraints
* 2 \leq N \leq 100
* 1 \leq A < B \leq N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N A B
Output
Print `Alice` if Alice wins, `Borys` if Borys wins, and `Draw` if nobody wins.
Examples
Input
5 2 4
Output
Alice
Input
2 1 2
Output
Borys
Input
58 23 42
Output
Borys | {"ground_truth": "{\"inputs\": [\"9 23 42\", \"8 2 4\", \"3 1 2\", \"9 23 18\", \"3 2 2\", \"8 2 3\", \"9 23 23\", \"0 2 2\", \"7 2 3\", \"9 44 23\", \"0 2 1\", \"7 2 5\", \"9 44 0\", \"0 0 1\", \"7 1 5\", \"9 38 0\", \"0 1 1\", \"7 1 4\", \"1 38 0\", \"0 1 0\", \"8 1 4\", \"1 38 1\", \"0 2 0\", \"8 1 7\", \"1 31 0\", \"0 0 0\", \"8 0 7\", \"2 31 0\", \"1 0 0\", \"8 0 3\", \"2 31 -1\", \"2 0 0\", \"8 1 3\", \"2 53 -1\", \"0 0 -1\", \"3 1 3\", \"2 64 -1\", \"0 -1 -1\", \"0 1 3\", \"0 64 -1\", \"-1 -1 -1\", \"-1 1 3\", \"0 64 0\", \"0 -2 -1\", \"-1 1 4\", \"1 64 0\", \"0 1 -1\", \"-1 1 7\", \"1 103 0\", \"1 1 -1\", \"-1 1 13\", \"1 103 1\", \"2 1 -1\", \"-1 1 2\", \"2 103 1\", \"4 1 -1\", \"0 1 2\", \"2 79 1\", \"4 1 0\", \"0 1 4\", \"2 79 2\", \"7 1 0\", \"0 1 6\", \"2 56 2\", \"7 0 0\", \"0 0 6\", \"2 56 4\", \"11 0 0\", \"-1 0 6\", \"2 12 4\", \"11 -1 0\", \"-1 0 8\", \"2 21 4\", \"21 -1 0\", \"-1 0 10\", \"2 21 0\", \"21 -2 0\", \"0 0 10\", \"2 35 0\", \"21 -2 1\", \"1 0 -1\", \"2 35 1\", \"16 -2 1\", \"1 -1 -1\", \"2 30 1\", \"16 -3 1\", \"2 -1 -1\", \"2 11 1\", \"16 -3 2\", \"2 -1 -2\", \"0 11 1\", \"5 -3 2\", \"0 -1 -2\", \"-1 11 1\", \"7 -3 2\", \"0 -1 -3\", \"-1 22 1\", \"13 -3 2\", \"0 0 -3\", \"-1 22 2\", \"58 23 42\", \"2 1 2\", \"5 2 4\"], \"outputs\": [\"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\\n\", \"Borys\\n\", \"Borys\\n\", \"Alice\\n\", \"Borys\", \"Borys\", \"Alice\"]}", "dataset_type": "taco"} |
taco_7430 | deepcoder | You have an array a of length n. For every positive integer x you are going to perform the following operation during the x-th second:
* Select some distinct indices i_{1}, i_{2}, …, i_{k} which are between 1 and n inclusive, and add 2^{x-1} to each corresponding position of a. Formally, a_{i_{j}} := a_{i_{j}} + 2^{x-1} for j = 1, 2, …, k. Note that you are allowed to not select any indices at all.
You have to make a nondecreasing as fast as possible. Find the smallest number T such that you can make the array nondecreasing after at most T seconds.
Array a is nondecreasing if and only if a_{1} ≤ a_{2} ≤ … ≤ a_{n}.
You have to answer t independent test cases.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.
The first line of each test case contains single integer n (1 ≤ n ≤ 10^{5}) — the length of array a. It is guaranteed that the sum of values of n over all test cases in the input does not exceed 10^{5}.
The second line of each test case contains n integers a_{1}, a_{2}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 10^{9}).
Output
For each test case, print the minimum number of seconds in which you can make a nondecreasing.
Example
Input
3
4
1 7 6 5
5
1 2 3 4 5
2
0 -4
Output
2
0
3
Note
In the first test case, if you select indices 3, 4 at the 1-st second and 4 at the 2-nd second, then a will become [1, 7, 7, 8]. There are some other possible ways to make a nondecreasing in 2 seconds, but you can't do it faster.
In the second test case, a is already nondecreasing, so answer is 0.
In the third test case, if you do nothing at first 2 seconds and select index 2 at the 3-rd second, a will become [0, 0]. | {"ground_truth": "{\"inputs\": [\"6\\n3\\n1000000000 0 -1000000000\\n1\\n6\\n2\\n-1000000000 1000000000\\n2\\n1000000000 -1000000000\\n2\\n1000000000 1000000000\\n2\\n-1000000000 -1000000000\\n\", \"6\\n3\\n1000000000 0 -1000000000\\n1\\n6\\n2\\n-1000000000 1000000000\\n2\\n1000000000 -1000000000\\n2\\n1000000000 1000000100\\n2\\n-1000000000 -1000000000\\n\", \"3\\n4\\n1 12 6 5\\n5\\n1 2 3 4 5\\n2\\n0 -4\\n\", \"3\\n4\\n1 12 6 5\\n5\\n1 2 3 4 5\\n2\\n-1 -4\\n\", \"3\\n4\\n1 7 6 5\\n5\\n1 2 3 4 5\\n2\\n0 -7\\n\", \"3\\n4\\n1 12 6 5\\n5\\n1 0 3 4 9\\n2\\n-1 -4\\n\", \"6\\n3\\n1000000100 0 -1000000000\\n1\\n6\\n2\\n-1000000000 1000000000\\n2\\n1000000000 -1000000000\\n2\\n1001000000 1000000000\\n2\\n-1000000000 -1000000000\\n\", \"3\\n4\\n1 7 6 5\\n5\\n1 2 1 4 5\\n2\\n0 -7\\n\", \"3\\n4\\n1 12 1 5\\n5\\n1 0 3 4 9\\n2\\n-1 -4\\n\", \"3\\n4\\n1 7 0 5\\n5\\n1 2 1 4 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taco_7431 | deepcoder | Captain Flint and his crew keep heading to a savage shore of Byteland for several months already, drinking rum and telling stories. In such moments uncle Bogdan often remembers his nephew Denis. Today, he has told a story about how Denis helped him to come up with an interesting problem and asked the crew to solve it.
In the beginning, uncle Bogdan wrote on a board a positive integer $x$ consisting of $n$ digits. After that, he wiped out $x$ and wrote integer $k$ instead, which was the concatenation of binary representations of digits $x$ consists of (without leading zeroes). For example, let $x = 729$, then $k = 111101001$ (since $7 = 111$, $2 = 10$, $9 = 1001$).
After some time, uncle Bogdan understood that he doesn't know what to do with $k$ and asked Denis to help. Denis decided to wipe last $n$ digits of $k$ and named the new number as $r$.
As a result, Denis proposed to find such integer $x$ of length $n$ that $r$ (as number) is maximum possible. If there are multiple valid $x$ then Denis is interested in the minimum one.
All crew members, including captain Flint himself, easily solved the task. All, except cabin boy Kostya, who was too drunk to think straight. But what about you?
Note: in this task, we compare integers ($x$ or $k$) as numbers (despite what representations they are written in), so $729 < 1999$ or $111 < 1000$.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases.
Next $t$ lines contain test cases — one per test case. The one and only line of each test case contains the single integer $n$ ($1 \le n \le 10^5$) — the length of the integer $x$ you need to find.
It's guaranteed that the sum of $n$ from all test cases doesn't exceed $2 \cdot 10^5$.
-----Output-----
For each test case, print the minimum integer $x$ of length $n$ such that obtained by Denis number $r$ is maximum possible.
-----Example-----
Input
2
1
3
Output
8
998
-----Note-----
In the second test case (with $n = 3$), if uncle Bogdan had $x = 998$ then $k = 100110011000$. Denis (by wiping last $n = 3$ digits) will obtain $r = 100110011$.
It can be proved that the $100110011$ is the maximum possible $r$ Denis can obtain and $998$ is the minimum $x$ to obtain it. | {"ground_truth": "{\"inputs\": [\"2\\n1\\n3\\n\", \"1\\n2\\n\", \"1\\n2\\n\", \"2\\n87911\\n94124\\n\", \"20\\n1057\\n7092\\n1990\\n3013\\n7002\\n18597\\n2726\\n6319\\n1248\\n5690\\n3467\\n4270\\n6973\\n2935\\n100000\\n19329\\n1836\\n1100\\n2599\\n2579\\n\", \"5\\n46809\\n40813\\n42036\\n43977\\n24229\\n\", \"2\\n100000\\n100000\\n\", \"1\\n4\\n\", \"2\\n18738\\n94124\\n\", \"5\\n46809\\n40813\\n44522\\n43977\\n24229\\n\", \"2\\n100000\\n100100\\n\", \"1\\n5\\n\", \"2\\n18105\\n94124\\n\", \"1\\n1\\n\", \"2\\n18105\\n165602\\n\", \"2\\n14792\\n165602\\n\", \"2\\n10729\\n165602\\n\", \"2\\n11405\\n165602\\n\", \"2\\n11405\\n1961\\n\", \"2\\n5649\\n1961\\n\", \"2\\n5649\\n213\\n\", \"2\\n5649\\n104\\n\", \"2\\n5649\\n171\\n\", \"2\\n3451\\n171\\n\", \"2\\n3547\\n171\\n\", \"2\\n76\\n171\\n\", \"2\\n87\\n171\\n\", \"2\\n87\\n336\\n\", \"2\\n87\\n24\\n\", 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\"999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999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\"8\\n998\\n\"]}", "dataset_type": "taco"} |
taco_7432 | deepcoder | Monocarp has forgotten the password to his mobile phone. The password consists of $4$ digits from $0$ to $9$ (note that it can start with the digit $0$).
Monocarp remembers that his password had exactly two different digits, and each of these digits appeared exactly two times in the password. Monocarp also remembers some digits which were definitely not used in the password.
You have to calculate the number of different sequences of $4$ digits that could be the password for Monocarp's mobile phone (i. e. these sequences should meet all constraints on Monocarp's password).
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($1 \le n \le 8$) — the number of digits for which Monocarp remembers that they were not used in the password.
The second line contains $n$ different integers $a_1, a_2, \dots a_n$ ($0 \le a_i \le 9$) representing the digits that were not used in the password. Note that the digits $a_1, a_2, \dots, a_n$ are given in ascending order.
-----Output-----
For each testcase, print one integer — the number of different $4$-digit sequences that meet the constraints.
-----Examples-----
Input
2
8
0 1 2 4 5 6 8 9
1
8
Output
6
216
-----Note-----
In the first example, all possible passwords are: "3377", "3737", "3773", "7337", "7373", "7733". | {"ground_truth": "{\"inputs\": [\"2\\n8\\n0 1 2 4 5 6 8 9\\n1\\n8\\n\", \"7\\n1\\n8\\n1\\n8\\n1\\n8\\n1\\n8\\n1\\n8\\n1\\n8\\n1\\n8\\n\", \"7\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n\", \"1\\n8\\n0 1 2 4 5 6 8 9\\n\", \"3\\n8\\n0 1 2 4 5 6 8 9\\n1\\n8\\n1\\n8\\n\", \"1\\n1\\n8\\n\", \"1\\n4\\n0 1 4 7\\n\", \"1\\n4\\n0 2 4 7\\n\", \"12\\n8\\n1 2 3 5 6 7 8 9\\n6\\n4 5 6 7 8 9\\n7\\n0 4 5 6 7 8 9\\n7\\n1 4 5 6 7 8 9\\n8\\n0 1 4 5 6 7 8 9\\n7\\n2 4 5 6 7 8 9\\n8\\n0 2 4 5 6 7 8 9\\n8\\n1 2 4 5 6 7 8 9\\n7\\n3 4 5 6 7 8 9\\n8\\n0 3 4 5 6 7 8 9\\n8\\n1 3 4 5 6 7 8 9\\n8\\n2 3 4 5 6 7 8 9\\n\"], \"outputs\": [\"6\\n216\\n\", \"216\\n216\\n216\\n216\\n216\\n216\\n216\\n\", \"216\\n216\\n216\\n216\\n216\\n216\\n216\\n\", \"6\\n\", \"6\\n216\\n216\\n\", \"216\\n\", \"90\\n\", \"90\\n\", \"6\\n36\\n18\\n18\\n6\\n18\\n6\\n6\\n18\\n6\\n6\\n6\\n\"]}", "dataset_type": "taco"} |
taco_7433 | deepcoder | The Hedgehog recently remembered one of his favorite childhood activities, — solving puzzles, and got into it with new vigor. He would sit day in, day out with his friend buried into thousands of tiny pieces of the picture, looking for the required items one by one.
Soon the Hedgehog came up with a brilliant idea: instead of buying ready-made puzzles, one can take his own large piece of paper with some picture and cut it into many small rectangular pieces, then mix them and solve the resulting puzzle, trying to piece together the picture. The resulting task is even more challenging than the classic puzzle: now all the fragments have the same rectangular shape, and one can assemble the puzzle only relying on the picture drawn on the pieces.
All puzzle pieces turn out to be of the same size X × Y, because the picture is cut first by horizontal cuts with the pitch of X, then with vertical cuts with the pitch of Y. If we denote the initial size of the picture as A × B, then A must be divisible by X and B must be divisible by Y (X and Y are integer numbers).
However, not every such cutting of the picture will result in a good puzzle. The Hedgehog finds a puzzle good if no two pieces in it are the same (It is allowed to rotate the pieces when comparing them, but it is forbidden to turn them over).
Your task is to count for a given picture the number of good puzzles that you can make from it, and also to find the puzzle with the minimal piece size.
Input
The first line contains two numbers A and B which are the sizes of the picture. They are positive integers not exceeding 20.
Then follow A lines containing B symbols each, describing the actual picture. The lines only contain uppercase English letters.
Output
In the first line print the number of possible good puzzles (in other words, the number of pairs (X, Y) such that the puzzle with the corresponding element sizes will be good). This number should always be positive, because the whole picture is a good puzzle itself.
In the second line print two numbers — the sizes X and Y of the smallest possible element among all good puzzles. The comparison is made firstly by the area XY of one element and secondly — by the length X.
Examples
Input
2 4
ABDC
ABDC
Output
3
2 1
Input
2 6
ABCCBA
ABCCBA
Output
1
2 6
Note
The picture in the first sample test has the following good puzzles: (2, 1), (2, 2), (2, 4). | {"ground_truth": "{\"inputs\": [\"12 18\\nCBBCAACABACCACABBC\\nABCAACABAABCBCBCCC\\nBCAACCCBBBABBACBBA\\nACCBCBBBAABACCACCC\\nCAABCCCACACCBACACC\\nBBBCBCACCABCCBCBBB\\nBAABBCACAAAAACCBCB\\nBAABAABACBCABACBCA\\nAABCBCCBCCABACCCAC\\nCCBBBAACCCBCACCCBB\\nCBABACBBBABCBACCCB\\nAABACCCBCCACBCACCB\\n\", \"10 11\\nABBBAABABBB\\nBBAABABBAAB\\nAABBBBBAAAA\\nBBABABAAABA\\nAABABBBAABB\\nAAABABAABAB\\nBBABBBABBBB\\nBBABABABBAA\\nBBABABAAABB\\nBABAABAABAB\\n\", \"14 16\\nCBCCCABCBBBAAACC\\nAABAACBACBCBACCA\\nABBBABAACCACCCCC\\nBBACACACCCCBBBAC\\nBBCAABACBAACBCAA\\nAAACCACBBCABABCB\\nABCBCAAAAACBABBA\\nAAABBBCCBAACBBCA\\nBBAACBABBBCCBAAC\\nBAABCCBAAABAACAC\\nABBBBCBAACACCBCB\\nBCABACBBBCAACACC\\nACCCCABCCCBBCAAC\\nBCBBCCCBCBCCACAA\\n\", \"9 9\\nIZHKRCRTM\\nLQBOENMNQ\\nYLNVFBFUY\\nACTTYWABL\\nYSEGWNQHC\\nTZASWPPAG\\nLLZTKFPMV\\nGXBETPPPN\\nUCPEFNJKN\\n\", \"16 16\\nACABBCCBAABCCCCB\\nAABCACCAAACACABB\\nBCCCAABBAACBACAA\\nBCACAABBBCAAAABA\\nACCBABCCACABBCCC\\nCCAAACACACBCABCA\\nBCAACBBBCACBBCAB\\nBABBCBBBCCCBAACC\\nBBBBBABACBABBCBA\\nABAACBACCACBBABA\\nABAACBACCBCBCCBB\\nBCACCCAABCBBCBCB\\nBBBCCCBCCBCBACCA\\nAABCBBBBACCACCBB\\nBCABCCCBCBBBCBCC\\nACCCCCCBBBAABACC\\n\", \"1 1\\nC\\n\", \"12 13\\nTHSGJEPTDFEIJ\\nOWPJGXSXJRYGD\\nVYENWXFWSOSMX\\nFZDFXFPWEIYYV\\nOEODFOGQWJEEU\\nSQRNSBTAMLQRU\\nLXGZERSWTJWQK\\nLGRJJMDTZVZWJ\\nDWVBTSZKFUAHT\\nHSSZHXAWVWMHB\\nJZOCNFUHTHQYV\\nTUHDMTZAQVWDL\\n\", \"12 11\\nBBAAAABBAAB\\nBBABBABBABB\\nBAABABBABBA\\nBABBBAAAABA\\nABBAABBBBBA\\nABBABBABABB\\nAAABBBABBBB\\nBAABAAABAAA\\nAAAABBBBABA\\nAAABAAABBBB\\nBAAAAABABAB\\nABBBBABABBB\\n\", \"5 5\\nABAAA\\nBBBAA\\nABABA\\nBBABB\\nBAAAB\\n\", \"5 5\\nDZEZF\\nOHZZC\\nCNDOX\\nNVYDP\\nUCIAX\\n\", \"4 6\\nABCDEF\\nGHIJKL\\nMNOPQR\\nSTUVWX\\n\", \"2 2\\nCC\\nBB\\n\", \"12 13\\nBBABABAAAAABA\\nABAAAAAAAABBA\\nABBBABAAAAABA\\nBBBAABABBABBB\\nABABAAABABABB\\nABBAABAABBAAA\\nAABABBAAABBAB\\nABBBBBABBAABA\\nBBBBBABBABBAA\\nAAAAAAABBBAAB\\nBAABBBAABAAAA\\nBBBBBBABABABA\\n\", \"17 17\\nBCBAAABAABCCCAAAC\\nBBAABCABBAACCACBB\\nABCCBAABBCCABBBAB\\nAACCBBACCAAACCACA\\nABBACBAAAABBABCAA\\nACBACCCABAABBCABB\\nCBCCCBCACBABCAAAA\\nAAABACACABABCCCBC\\nCABABBABBBABBBCAB\\nBCBCBAAACCCACACBA\\nBBACABACAAABCCBBC\\nABAABBABCCAABBCCA\\nAABBACBCBCCBAACBB\\nBBABCBBCCCBCACBCB\\nBABCBBCCABCABBAAA\\nAABAABBBBAACAABCC\\nBACCCBBCCABBBACBB\\n\", \"18 19\\nLEXQWPUXGOWSELHIQPY\\nZUYPTUDHEEQVRWBCXBU\\nZUPMYQQQFHGKZZDMLFM\\nCASSUVIKQKCEALUDDFK\\nFDBZOXULVGFARYPNAQY\\nWEFLTZOSOAGAMBWNGVC\\nEVAPNTSSIMKNBOAHFSC\\nUHTWEBRCEUJSARNEWYI\\nGXGSDCDUIWYQRZUPQBZ\\nFMYJUOHENURMDINJGCN\\nHIBATJCOGWWRQWTLXDH\\nRDDXJNZHQGUWPNGIDRO\\nAJGHDUCGGLPYYDYSFRS\\nAZGBVLJYYZWSQGBFJVU\\nQJJRSHZFOECHGRGALML\\nJKDMLPREFTISSSAJKJN\\nGRHGVYSVQLYKCIMBIKA\\nMSHRBZJJLDHBCAWAJBN\\n\", \"16 15\\nPFUMRKDISIBBVYP\\nMZKXWWSQXADAPEB\\nVTBYXGWQYZTHBHY\\nONGURZKWHZDKIDF\\nGCMHQQNJJXHHPVU\\nNLMUXXKZOFNMFTG\\nANDDDPHEDVWVHLC\\nOYGXUHIMYPNIXCT\\nILCGDQZNCSTIILX\\nZVSYMJBHAUEXZMY\\nMYOKFPJKKJLKVWI\\nUEMUOOAJSNTOLEN\\nLKIROZUNWRZBMZP\\nYYWCXLGHLZQVPOB\\nFMHPKABCBAAYCFA\\nNRGFEWPLKNORSZR\\n\", \"2 2\\nAB\\nCD\\n\", \"14 12\\nBBAAABBBAAAB\\nBBABAAAAABAA\\nAABBABBBABBA\\nBABAABAABBBB\\nBBBABBBBABAA\\nABBAABBAAABA\\nABAAAAABBBAB\\nBBAABBABBBAA\\nBAABABAAABAB\\nAAABBBABBABA\\nBABBBBAABBBA\\nAAAAABABBAAB\\nBABBBABBBBBA\\nBAAAABAABAAA\\n\", \"20 18\\nNLBILWYVJJLCACSMUA\\nAAMAWVGEZDTWUUZNMM\\nWWNOTPPFXJSWWSPPRB\\nYUJXZSHHNFGKXIXEJN\\nLTKNJOJALEQURSYVBI\\nSVXHFTUYWTLBXWFDXD\\nLQUEBPXELRNAXFIKFT\\nZGZEPWGVLVNMQVRMJM\\nWTMIPWRNQCWKZACSKQ\\nYGUREEGHTVMICOCUHE\\nUNIJGNPINIFWCIHGIQ\\nIRGJEHFRUJOHIXRSLF\\nDQVCPHUSKYEHFGWBPS\\nJIIGNJKTRAAPRBOGMQ\\nHFNGDLVBUVECUMQDMT\\nGEGCSOPRXQAEMDQAYO\\nOHSBTADOWBVKZINKXC\\nIIPWCAZSNDFVBMTGMI\\nOZZTLUOFRYDNTPIAVA\\nTFBGPAMJPIWLEZOKXB\\n\", \"2 14\\nAABACBACBCBBCB\\nBACCBBBCBAABBC\\n\", \"16 4\\nBAAC\\nBACA\\nACBC\\nABCC\\nCCAC\\nBBCC\\nCCAB\\nABCC\\nCBCA\\nBCBC\\nBCBC\\nCBBB\\nBBAA\\nBACA\\nABCB\\nAABA\\n\", \"14 13\\nBGBALYLHQYMFM\\nRLFOZFDFMRFEN\\nGDWROOMXUVBOW\\nDPXWRDPCEFMRQ\\nJOSEGKGMHGHFC\\nJHXUBTPOZOYGJ\\nFHUUMHWSQRNEP\\nVGWYMTMWHWGIL\\nVMWDTBDJGEVZI\\nLEJSIHTQKYDXY\\nOLUOIWECMZVAI\\nVDXSGRPMCCJEM\\nMYWMDDAQAPBSG\\nXQWPFRAPVEOYO\\n\", \"16 17\\nFFOYWWWJRUPVBGSSJ\\nVPOMWQMWUWYMMDAPB\\nARQUYXZTHVSQZHMVJ\\nCJAGELECYEXSHEYTU\\nXRSZPRCBQPJQACNWR\\nJISALKDCKJUWWHMYH\\nGMISALZMLGRRGALJA\\nCWPYTQYBXKLBGWKNF\\nMJJYWBIHJLARHFNWB\\nKEREXXISTPANXGGJG\\nLECEJLPAFOZHLRTJM\\nHBOWFNSQFRRGEJFMJ\\nVEGIRVEXACMJVKFYN\\nSCGOPQKUHEDNIPIRE\\nLENRPPYJBEVDTOPOY\\nFHJOESUHLIJRFPVBK\\n\", \"2 4\\nABAA\\nABBB\\n\", \"6 7\\nGYSGYUL\\nKGTJUVI\\nFNRHOND\\nZGZAFYZ\\nQVCRZCA\\nJCCXKGV\\n\", \"20 18\\nAABCAACCBBCBABBBBB\\nBBCBAACCBCAACBBCCB\\nACCBABABACBBACBBAB\\nACBBBCBAAACAAAAABB\\nBCBABABAACCCABBBCC\\nBAAAAAACACABBCCCAC\\nCBACCBCBACACAAACBC\\nCBACAACBCBCAACACCA\\nCCCBACCBACACCCBCCB\\nCACABBBBBBCCBACCBA\\nCCBCACABCBACABBCCB\\nAACACCCCCABAABCACC\\nCBBACCBBCBCBBCCAAB\\nCABBABACCABACAABAB\\nBBBABBCBCBACBCCABA\\nBCCAACBCBCAAAABACA\\nAAABACBBCCCACACBAC\\nBABAAAACCBACBACAAA\\nAABBABCBBBACAACBAB\\nBBABBAABACBAABCCBB\\n\", \"4 6\\nABABAC\\nBABABC\\nABABAC\\nCCCCCA\\n\", \"4 4\\nACAC\\nCBCC\\nABBC\\nCCAC\\n\", \"1 1\\nZ\\n\", \"5 6\\nBBBABB\\nAAAABB\\nABABAA\\nABBBAA\\nBABBBA\\n\", \"4 3\\nOKJ\\nXTV\\nDVW\\nHMK\\n\", \"7 7\\nBBAAABB\\nAABBBBA\\nAABABBA\\nAABABAB\\nAABBBAA\\nBAAAABA\\nBBABBBB\\n\", \"19 19\\nACCACBCABACABCACCAA\\nBCACAAAACCACCCCBCCB\\nCBACBBCBCBCABCABACA\\nAACCAABBBCAAABACAAC\\nACACCCBBBACACCAAABA\\nAACAABCACCBCACCABBA\\nAABBCCABACCACABACAA\\nACBCCACBACCACABCABC\\nAACAABCAACCBBAACBCA\\nAAACACBAABCBACCAAAB\\nAABACABBABCACAACBCA\\nBABAAABCACBABACBBBC\\nBAABCAAABCAABBCCAAC\\nBCABCCBCCBCBABCBCCA\\nBACACBACBCABBCBCABB\\nABCACCBBBBCBBCABAAC\\nBBBBCCBCBACAACBCBCA\\nAAABBBBCACCACCAAACC\\nCCCCCBAABAAAACCCBBA\\n\", \"3 3\\nACA\\nCCA\\nACB\\n\", \"5 5\\nBBCAB\\nBCBAC\\nCAAAB\\nACBBA\\nCAACB\\n\", \"1 12\\nABAAADCAAABX\\n\", \"17 17\\nBBAABAABBBBBAABBB\\nBBABABBBBABAAABBB\\nAAAABAAAABABABBAA\\nBBABAAABBABBAAABA\\nAAABBBBBAABABBBAB\\nAABBBBBABABABABBB\\nBAABAAABAAABBAABB\\nBBAAAAAABABABBAAB\\nAAAAABAABBAAAABAA\\nBABAABABABABABBBB\\nBAABABBAAABBAAABB\\nABBAAABBBBAAAABAB\\nBBABAABAAAAAABBBB\\nAAABBABBAAAAABBBB\\nAABAABBAABBABAABB\\nABABAAABBABAAABAB\\nBBABABBBAAAAAAABA\\n\", \"8 9\\nBAABABAAB\\nBAABAAAAB\\nBBBBBAABB\\nAAAAAAAAB\\nBABBABBAA\\nBBABABBBB\\nBABABBAAA\\nAABAABBBB\\n\", \"8 8\\nTNMIIMOP\\nJOAXSHVN\\nQYHMVXGM\\nQOXAIUMI\\nLAAXNKCH\\nORWESZUV\\nPMIXHLEA\\nAENPGVYK\\n\", \"14 10\\nABBAAABBAA\\nBBBBBABBAA\\nBABABBABAB\\nAAABABBAAB\\nBBABABBBAB\\nBBABBABABB\\nAABBBBABAA\\nABBBAAAABB\\nABBABAABAA\\nABABABABBA\\nABAABBBAAB\\nAAAAAAAAAA\\nABABBAABAA\\nBABAABABBB\\n\", \"14 17\\nXGFETCAWEBHYYDECE\\nCGFEUQEYMLSVHNKJA\\nZMGSXZJASBUPTHRFQ\\nGQREDKHDBTZPGWHEO\\nQGACDHZVBAOGLHHEL\\nLKLKVFVDHSRQNEDXC\\nVNREYHZDJHPJKHXDO\\nKBOMZYHZEUOYUOXSQ\\nFNQGOBVDBTMUJPAKU\\nXFPGQQXBPELKWSXCJ\\nABUKLBPTFOGUJFDEQ\\nKXPJEZJQCHTENYSKY\\nXXOKEXESEVLQMFDZG\\nVPGUBSJLGBWZWAMFZ\\n\", \"2 2\\nML\\nWQ\\n\", \"14 15\\nJFLSOQHVDRTCPWZ\\nWSROLOOQOCWPJNX\\nEEUZVBLQXBFQKNA\\nQIGZDIMDXVCHJFJ\\nUDJGIZWDBMMMBJR\\nEWXAQHPRYBQOYDT\\nUDEAPOBVZOXNVMK\\nAYEVKFIKNRUVRQC\\nNLTLJBXWMUQXAZD\\nKOXESBBUYLMIDOI\\nZOJWEOJFCYTILHE\\nRQDNTBZZXPKNCEN\\nSYGFASAQUSMYYRP\\nUOYCFYUDACJDTAD\\n\", \"6 6\\nCCABCA\\nBCBCBC\\nBAAAAA\\nCBBCAA\\nACBBCA\\nCCAABA\\n\", \"4 8\\nCACABCCA\\nABCBAACA\\nACABBBCC\\nAACCBCBB\\n\", \"16 16\\nABBABBABBAABBBAB\\nBABABBAABAABBAAA\\nBAAABBAABAABBBAA\\nAABAAAABAAAABBBA\\nBAAAABAABBBABBAA\\nAABBABABABAABBBA\\nBABBBABAAAAABABB\\nBABBBBBBBBABBBAB\\nBAAAABBBABAABBBA\\nBABBBABBAABABBAA\\nBBBBBBAABBBABBBA\\nBABAAAABAABAABBB\\nAAAAABBAAABABAAA\\nBABBABABABAAABAB\\nBAAAAAAAABBABAAA\\nBAAAAABABBBBAAAA\\n\", \"6 6\\nQLXBOE\\nKEEYTR\\nZLPMSP\\nWOKAHN\\nLYXBXU\\nSZOEZV\\n\", \"8 7\\nBABABBB\\nABABABA\\nAABBABA\\nABBABAA\\nBABAAAB\\nAABBBBA\\nABBBBAB\\nBBAAABA\\n\", \"18 18\\nBBBBBBBABABBBABABA\\nBAAABAAABBBABABBBB\\nBABBAAABAAABAAABAA\\nAABBABBBABBBBBAAAB\\nBBBAAAAABBABBAAAAA\\nAABBAABABABBBABABA\\nBAABBAAAABABAABABB\\nBABBABBBAAAABAABBA\\nBBBBAABAAABAAABBBA\\nABABBAAABBBBBABABA\\nABABAABBBBBABBBBBB\\nABAAABBABBABAAAABA\\nBABAAABABABBBABBBB\\nBBBBABBBABBBBBBBBA\\nBAAABAABABABBBBAAB\\nBABBAABABBABAABBBB\\nBAABABAAAABBABBAAA\\nBAAABBBAABABBABBAB\\n\", \"20 20\\nABBBAAABABAAAAABBABB\\nBABABBAABAABBAAABABB\\nBABBBAABAABBABBBBABA\\nBAAABBAAABABBABBAAAA\\nABBAABAABBBBAAABBBAA\\nBAAAAAAAABABBAAAAABB\\nAAAAAAABABBBBBAABAAB\\nABBBBABAABBAAAAABAAA\\nBAAAAABBABAAAAABAAAB\\nABABAABABBBABBAABBAA\\nBAAABBBAAAABBBBBABAA\\nAAABBABABAABBABAABAB\\nABBABABABABAAABABABA\\nBAABAAAAABBAABBBAAAB\\nABAAABBABAABBBABAABA\\nBAABBBBBABBBABBBABAB\\nBABBABABBBBBBBBABAAA\\nABAAABAAABAAABABABAA\\nBAABBBBAABBAAAAAABBA\\nABAABBABAAABBABABAAA\\n\", \"16 15\\nABBBBAAABABBABB\\nABBBAAABBABBBBB\\nBABABAABBBABABB\\nAAABBBBBABBABBB\\nBAABAABAABAABBA\\nABBBBAAAAAAAABB\\nBAABBBABABAAAAB\\nAAAABBAABBAABAA\\nABBABABAAABABBB\\nAAABBBABAABABAA\\nBAABABBAAABBAAA\\nAAAAAAABABBBAAA\\nBABBAABBABAAAAB\\nABABAAABBBBBAAB\\nBBABBAABABAABBB\\nBAAAABBBABABBBA\\n\", \"10 10\\nABBAABAABB\\nABAAAAAABA\\nBAABABABAA\\nBAAAAAAAAB\\nBABABBBAAB\\nABBABBBBBA\\nAABABAAAAA\\nBAAAABAABA\\nABABAABBAA\\nBBABBABABB\\n\", \"3 3\\nBXP\\nUJF\\nAQT\\n\", \"9 10\\nXHPCDAAFPZ\\nJRZCDTQBYP\\nZBTAMDPIFY\\nXBKTMXNIWM\\nDAIONPEBYF\\nAFHBCBDTKB\\nKRVEBSUXRM\\nWGMEZTWDBX\\nNOJUCDZPZY\\n\", \"10 11\\nABBBAABABBB\\nBBAABABBAAB\\nAABBBBBAAAA\\nBBABABAAABA\\nAAAABBBAABB\\nAAABABAABAB\\nBBABBBABBBB\\nBBABABABBAA\\nBBABABAAABB\\nBABAABAABAB\\n\", \"14 16\\nCBCCCABCBBBAAACC\\nAABAACBACBCBACCA\\nABBBABAACCACCCCC\\nBBACABACCCCBBBAC\\nBBCAABACBAACBCAA\\nAAACCACBBCABABCB\\nABCBCAAAAACBABBA\\nAAABBBCCBAACBBCA\\nBBAACBABBBCCBAAC\\nBAABCCBAAABAACAC\\nABBBBCBAACACCBCB\\nBCABACBBBCAACACC\\nACCCCABCCCBBCAAC\\nBCBBCCCBCBCCACAA\\n\", \"9 9\\nMTRCRKHZI\\nLQBOENMNQ\\nYLNVFBFUY\\nACTTYWABL\\nYSEGWNQHC\\nTZASWPPAG\\nLLZTKFPMV\\nGXBETPPPN\\nUCPEFNJKN\\n\", \"12 13\\nTHSGJEPTDFEIJ\\nOWPJGXSXJRYGD\\nVYENWXFWSOSMX\\nFZDFXFPWEIYYV\\nOEODFOGQWJEEU\\nSQRNSBTAMLQRU\\nLXGZERSWTJWQK\\nLGRJJMDTZVZWJ\\nDWVBTSZKFUAHT\\nHSSZHXAWVWMHB\\nVYQHTHUFNCOZJ\\nTUHDMTZAQVWDL\\n\", \"5 5\\nABAAA\\nBBBAA\\nABABA\\nBBABB\\nBAAAC\\n\", \"12 13\\nBBABABAAAAABA\\nABAAAAAAAABBA\\nABBBABAAAAABA\\nBBAAABABBBBBB\\nABABAAABABABB\\nABBAABAABBAAA\\nAABABBAAABBAB\\nABBBBBABBAABA\\nBBBBBABBABBAA\\nAAAAAAABBBAAB\\nBAABBBAABAAAA\\nBBBBBBABABABA\\n\", \"17 17\\nBCBAAABAABCCCAAAC\\nBBAABCABBAACCACBB\\nABCCBAABBCCABBBAB\\nAACCBBACCAAACCACA\\nABBACBAAAABBABCAA\\nACBACCCABAABBCABB\\nCBCCCBCACBABCAAAA\\nAAABACACABABCCCBC\\nCABABBABBBABBBCAB\\nABCACACCCAAABCBCB\\nBBACABACAAABCCBBC\\nABAABBABCCAABBCCA\\nAABBACBCBCCBAACBB\\nBBABCBBCCCBCACBCB\\nBABCBBCCABCABBAAA\\nAABAABBBBAACAABCC\\nBACCCBBCCABBBACBB\\n\", \"2 2\\nAB\\nDD\\n\", \"20 18\\nNLBILWYVJJLCACSMUA\\nAAMAWVGEZDTWUUZNMM\\nWWNOTPPFXJSWWSPPRB\\nYUJXZSHHNFGKXIXEJN\\nLTKNJOJALEQURSYVBI\\nSVXHFTUYWTLBXWFDXD\\nLQUEBPXELRNAXFIKFT\\nZGZEPWGVLVNMQVRMJM\\nWTMIPWRNQCWKZACSKQ\\nYGUREEGHTVMICOCUHE\\nUNIJGNPINIFWCIHGIQ\\nIRGJEHFRUJOHIXRSLF\\nDQVCPHUSKYEHFGWBPS\\nJIIGNJKTRAAPRBOGMQ\\nHFNGDLVBUVECUMQDMT\\nGEGCSOPRXQAEMDQAYO\\nOHSBTADOWBVKZINKXC\\nIIPWCAZSNDFVBMTGMI\\nOZZTLUOFRYDNTPIAVA\\nTFBGPAMJPIWLDZOKXB\\n\", \"16 4\\nBAAC\\nBACA\\nACBC\\nABCC\\nCCAC\\nBBCC\\nCCAB\\nABCC\\nCBCA\\nBCBC\\nBCBC\\nCBBA\\nBBAA\\nBACA\\nABCB\\nAABA\\n\", \"14 13\\nBGBALYLHQYMFM\\nRLFOZFDFMRFEN\\nGDWROOMXUVBOW\\nDPXWRDPCEFMRQ\\nJOSEGKGMHGHFC\\nJHXUBTPOZOYGJ\\nFHUUMHWSQRNEP\\nVGWYMTMWHWGIL\\nVMWDTBDJGEVZI\\nYXDYKQTHISJEL\\nOLUOIWECMZVAI\\nVDXSGRPMCCJEM\\nMYWMDDAQAPBSG\\nXQWPFRAPVEOYO\\n\", \"16 17\\nFFOYWWWJRUPVBGSSJ\\nVPOMWQMWUWYMMDAPB\\nARQUYXZTHVSQZHMVJ\\nCJAGELECYEXSHEYTU\\nXRSZPRCBQPJRACNWR\\nJISALKDCKJUWWHMYH\\nGMISALZMLGRRGALJA\\nCWPYTQYBXKLBGWKNF\\nMJJYWBIHJLARHFNWB\\nKEREXXISTPANXGGJG\\nLECEJLPAFOZHLRTJM\\nHBOWFNSQFRRGEJFMJ\\nVEGIRVEXACMJVKFYN\\nSCGOPQKUHEDNIPIRE\\nLENRPPYJBEVDTOPOY\\nFHJOESUHLIJRFPVBK\\n\", \"2 4\\nAAAA\\nABBB\\n\", \"6 7\\nGYSGYUL\\nKGTJUVI\\nFNRHOND\\nZGZAFYZ\\nQVCRACZ\\nJCCXKGV\\n\", \"5 6\\nBBBABB\\nAAAABB\\nAABABA\\nABBBAA\\nBABBBA\\n\", \"4 3\\nOKJ\\nVTX\\nDVW\\nHMK\\n\", \"7 7\\nBBAAABB\\nAABBBBA\\nAABABBA\\nAABABAC\\nAABBBAA\\nBAAAABA\\nBBABBBB\\n\", \"19 19\\nACCACBCABACABCACCAA\\nBCACAAAACCACCCCBCCB\\nABACBBCBCBCABCCBACA\\nAACCAABBBCAAABACAAC\\nACACCCBBBACACCAAABA\\nAACAABCACCBCACCABBA\\nAABBCCABACCACABACAA\\nACBCCACBACCACABCABC\\nAACAABCAACCBBAACBCA\\nAAACACBAABCBACCAAAB\\nAABACABBABCACAACBCA\\nBABAAABCACBABACBBBC\\nBAABCAAABCAABBCCAAC\\nBCABCCBCCBCBABCBCCA\\nBACACBACBCABBCBCABB\\nABCACCBBBBCBBCABAAC\\nBBBBCCBCBACAACBCBCA\\nAAABBBBCACCACCAAACC\\nCCCCCBAABAAAACCCBBA\\n\", \"8 8\\nTNMIIMOP\\nJOAXSHVN\\nQYHMVXGM\\nIMUIAXOQ\\nLAAXNKCH\\nORWESZUV\\nPMIXHLEA\\nAENPGVYK\\n\", \"14 10\\nABBAAABBAA\\nBBBBBABBAA\\nBABABBABAB\\nAAABABBAAB\\nBBABABBBAB\\nBABBBABABB\\nAABBBBABAA\\nABBBAAAABB\\nABBABAABAA\\nABABABABBA\\nABAABBBAAB\\nAAAAAAAAAA\\nABABBAABAA\\nBABAABABBB\\n\", \"14 15\\nJFLSOQHVDRTCPWZ\\nWSROLOOQOCWPJNX\\nEEUZVBLQXBFQKNA\\nQIGZDIMDXVCHJFJ\\nUDJGIZWDBMMMBJR\\nEWXAQHPRYBQOYDT\\nUDEAPOBVZOXNVMK\\nAYEVKFIKNRUVRQC\\nNLTLJBXWMUQXAZD\\nKOXESBBUYLMIDOI\\nZOJWEOJFCYTILHE\\nRQDNTBZZXPKNCEN\\nSYGFBSAQUSMYYRP\\nUOYCFYUDACJDTAD\\n\", \"6 6\\nQLXBOE\\nKEEYTR\\nZLPMSP\\nWOKAHN\\nUXBXYL\\nSZOEZV\\n\", \"8 7\\nBABABBB\\nABABABA\\nAACBABA\\nABBABAA\\nBABAAAB\\nAABBBBA\\nABBBBAB\\nBBAAABA\\n\", \"18 18\\nBBBBBBBABABBBABABA\\nBAAABAAABBBABABBBB\\nBABBAAABAAABAAABAA\\nAABBABBBABBBBBAAAB\\nBBBAAAAABBABBAAAAA\\nAABBAABABABBBABABA\\nBAABBAAAABABAABABB\\nBABBABBBAAAABAABBA\\nBBBBAABAAABAAABBBA\\nABABBAAABBBBBABABA\\nABABAABBBBBABBBBBB\\nABAAABBABBABAAAABA\\nBABAAABABABBBABBBB\\nABBBBBBBBABBBABBBB\\nBAAABAABABABBBBAAB\\nBABBAABABBABAABBBB\\nBAABABAAAABBABBAAA\\nBAAABBBAABABBABBAB\\n\", \"20 20\\nABCBAAABABAAAAABBABB\\nBABABBAABAABBAAABABB\\nBABBBAABAABBABBBBABA\\nBAAABBAAABABBABBAAAA\\nABBAABAABBBBAAABBBAA\\nBAAAAAAAABABBAAAAABB\\nAAAAAAABABBBBBAABAAB\\nABBBBABAABBAAAAABAAA\\nBAAAAABBABAAAAABAAAB\\nABABAABABBBABBAABBAA\\nBAAABBBAAAABBBBBABAA\\nAAABBABABAABBABAABAB\\nABBABABABABAAABABABA\\nBAABAAAAABBAABBBAAAB\\nABAAABBABAABBBABAABA\\nBAABBBBBABBBABBBABAB\\nBABBABABBBBBBBBABAAA\\nABAAABAAABAAABABABAA\\nBAABBBBAABBAAAAAABBA\\nABAABBABAAABBABABAAA\\n\", \"10 10\\nABBAABAABB\\nABAAAAAABA\\nBAABABABAA\\nBAAAAAAAAB\\nBABABBBAAB\\nABBABBBBBA\\nAAAAABABAA\\nBAAAABAABA\\nABABAABBAA\\nBBABBABABB\\n\", \"2 4\\nABDD\\nABDC\\n\", \"14 16\\nCBCCCABCBBBAAACC\\nAABAACBACBCBACCA\\nABBBABAACCACCCCC\\nBBACABACCCCBBBAC\\nBBCAABACBAACBCAA\\nAAACCACBBCABABCB\\nABCBCAAAAACBABBA\\nAAABBBCCBAACBBCA\\nBBAACBABBBCCBAAC\\nBAABCCBAAABAACAC\\nABBBBCBAACACCBCB\\nCCACAACBBBCABACB\\nACCCCABCCCBBCAAC\\nBCBBCCCBCBCCACAA\\n\", \"18 19\\nLEXQWPUXGOWSELHIQPY\\nZUYPTUDHEEQVRWBCXBU\\nZUPMYQQQFHGKZZDMLFM\\nCASSUVIKQKCEALUDDFK\\nFDBZOXULVGFARYPNAQY\\nWEFLTZOSOAGAMBWNGVC\\nEVAPNTSSIMKNBOAHFSC\\nUHTWEBRCEUJSARNEWYI\\nGXGSDCDUIWYQRZUPQBZ\\nFMYJUNHENURMDINJGCN\\nHIBATJCOGWWRQWTLXDH\\nRDDXJNZHQGUWPNGIDRO\\nAJGHDUCGGLPYYDYSFRS\\nAZGBVLJYYZWSQGBFJVU\\nQJJRSHZFOECHGRGALML\\nJKDMLPREFTISSSAJKJN\\nGRHGVYSVQLYKCIMBIKA\\nMSHRBZJJLDHBCAWAJBN\\n\", \"5 5\\nBBCAB\\nBCBAC\\nCAAAB\\nACBBA\\nCBACA\\n\", \"14 17\\nXGFETCAWEBHYYDECE\\nCGFEUQEYMLSVHNKJA\\nZMGSXZJASBUPTHRFQ\\nGQREDKHDBTZPGWHEO\\nQGACDHZVBAOGLHHEL\\nLKLKVFVDHSRQNEDXC\\nVNREYHZDJHPJKHXDO\\nKBOMZYHZEUOYUOXSQ\\nGNQGOBVDBTMUJPAKU\\nXFPGQQXBPELKWSXCJ\\nABUKLBPTFOGUJFDEQ\\nKXPJEZJQCHTENYSKY\\nXXOKEXESEVLQMFDZG\\nVPGUBSJLGBWZWAMFZ\\n\", \"10 11\\nABBBAABABBB\\nBBAABABBAAB\\nAABBBBBAAAA\\nBBABABAAABA\\nAAAABBBAABB\\nAAABABAABAB\\nBBABBBABBBB\\nBBAAABABBAA\\nBBABABAAABB\\nBABAABAABAB\\n\", \"9 9\\nMTRCRKHZI\\nLQBOENMNQ\\nYLNVFBFUY\\nACTTYWABL\\nYSEGWNQHC\\nTZASWPPAG\\nLLZVKFPMT\\nGXBETPPPN\\nUCPEFNJKN\\n\", \"12 13\\nTHSGJEPTDFEIJ\\nOWPJGXSXJRYGD\\nVYENWXFWSOSMX\\nFZDFXFPWEIYYV\\nUEEJWQGOFDOEO\\nSQRNSBTAMLQRU\\nLXGZERSWTJWQK\\nLGRJJMDTZVZWJ\\nDWVBTSZKFUAHT\\nHSSZHXAWVWMHB\\nVYQHTHUFNCOZJ\\nTUHDMTZAQVWDL\\n\", \"5 5\\nABAAA\\nBBBAA\\nABABA\\nCBABB\\nBAAAC\\n\", \"12 13\\nBBABABAAAAABA\\nABAAAAAAAABBA\\nABBBABAAAAABA\\nBBAAABABBBBBB\\nABABAAABABABB\\nABBAABAABBAAA\\nAABABBAAABBAB\\nABBBBBABBAABB\\nBBBBBABBABBAA\\nAAAAAAABBBAAB\\nBAABBBAABAAAA\\nBBBBBBABABABA\\n\", \"17 17\\nBCBAAABAABCCCAAAC\\nBBAABCABBAACCACBB\\nABCCBAABBCCABBBAB\\nAADCBBACCAAACCACA\\nABBACBAAAABBABCAA\\nACBACCCABAABBCABB\\nCBCCCBCACBABCAAAA\\nAAABACACABABCCCBC\\nCABABBABBBABBBCAB\\nABCACACCCAAABCBCB\\nBBACABACAAABCCBBC\\nABAABBABCCAABBCCA\\nAABBACBCBCCBAACBB\\nBBABCBBCCCBCACBCB\\nBABCBBCCABCABBAAA\\nAABAABBBBAACAABCC\\nBACCCBBCCABBBACBB\\n\", \"18 19\\nLEXQWPUXGOWSELHIQPY\\nZUYPTUDHEEQVRWBCXBU\\nZUPMYQQQFHGKZZDMLFM\\nCBSSUVIKQKCEALUDDFK\\nFDBZOXULVGFARYPNAQY\\nWEFLTZOSOAGAMBWNGVC\\nEVAPNTSSIMKNBOAHFSC\\nUHTWEBRCEUJSARNEWYI\\nGXGSDCDUIWYQRZUPQBZ\\nFMYJUNHENURMDINJGCN\\nHIBATJCOGWWRQWTLXDH\\nRDDXJNZHQGUWPNGIDRO\\nAJGHDUCGGLPYYDYSFRS\\nAZGBVLJYYZWSQGBFJVU\\nQJJRSHZFOECHGRGALML\\nJKDMLPREFTISSSAJKJN\\nGRHGVYSVQLYKCIMBIKA\\nMSHRBZJJLDHBCAWAJBN\\n\", \"20 18\\nNLBILWYVJJLCACSMUA\\nAAMAWVGEZDTWUUZNMM\\nWWNOTPPFXJSWWSPPRB\\nYUJXZSHHNFGKXIXEJN\\nLTKNJOJALEQURSYVBI\\nSVXHFTUYWTLBXWFDXD\\nLQUEBPXELRNAXFIKFT\\nZGZEPWGVLVNMQVRMJM\\nWTMIPWRNQCWKZACSKQ\\nYGUREEGHTVMICOCUHE\\nUNIJGNPINIFWCIHGIQ\\nIRGJEHFRUJOHIXRSLF\\nDQVCPHUSKYEHFGWBPS\\nJIIGNJKTRAAPRBOGMQ\\nHFNGDLVBUVECUMQDMT\\nGEGCSOPRXQAEMDQAYO\\nOHSBTADOWBVKZINKXC\\nIIPWCAZSNDFVBMTGMI\\nOZZTLUOFRYDNTPIAVA\\nTFBGPAMJPIWLDZPKXB\\n\", \"16 4\\nBAAC\\nBACA\\nACBC\\nABCC\\nCCAC\\nBBCC\\nCCAB\\nABCC\\nCBCA\\nBCBC\\nBCBC\\nCBBA\\nBBAA\\nBACA\\nABCB\\nABAA\\n\", \"14 13\\nBGBALYLHQYMFM\\nRLFOZFDFMRFEN\\nGDWROOMXUVBOW\\nDPXWRDPCEFMRQ\\nJOSEGKGMHGHFC\\nJHXUBTPOZOYGJ\\nFHUUMHWSQRNEP\\nVGWYMTMWHWGIL\\nVMWDTBDJGEVZI\\nYXDYKQTHISJEL\\nOLUOIWECMZVAI\\nVDXSGRPMCCJEM\\nMYWMDDQAAPBSG\\nXQWPFRAPVEOYO\\n\", \"16 17\\nFFOYWWWJRUPVBGSSJ\\nVPOMWQMWUWYMMDAPB\\nARQUYXZTHVSQZHMVJ\\nCJAGELECYEXSHEYTU\\nXRSZPRCBQPJRACNWR\\nJISALKDCKJUWWHMYH\\nGMISALZMLGRRGALJA\\nCWPYTQYBXKLBGWKNF\\nMJJYWBIHJLARHFNWB\\nKEREXXISTPANXGGJG\\nLECEJLPAFOZHLRTJM\\nHBOWFNSQFRRGEJFMJ\\nVEGIRVEXACMJVKFYN\\nSCGOPQKUHEDNIPIRE\\nYOPOTDVEBJYPPRNEL\\nFHJOESUHLIJRFPVBK\\n\", \"2 4\\nABDC\\nABDC\\n\", \"2 6\\nABCCBA\\nABCCBA\\n\"], \"outputs\": [\"24\\n4 2\\n\", \"5\\n10 1\\n\", \"15\\n7 1\\n\", \"8\\n1 3\\n\", \"17\\n4 2\\n\", \"1\\n1 1\\n\", \"10\\n3 1\\n\", \"7\\n1 11\\n\", \"3\\n1 5\\n\", \"3\\n1 5\\n\", \"12\\n1 1\\n\", \"2\\n1 2\\n\", \"7\\n12 1\\n\", \"3\\n1 17\\n\", \"10\\n3 1\\n\", \"18\\n1 3\\n\", \"4\\n1 1\\n\", \"14\\n1 12\\n\", \"33\\n1 3\\n\", \"4\\n1 7\\n\", \"9\\n2 4\\n\", \"6\\n7 1\\n\", \"8\\n4 1\\n\", \"2\\n1 4\\n\", \"7\\n2 1\\n\", \"27\\n4 2\\n\", \"4\\n2 3\\n\", \"5\\n1 4\\n\", \"1\\n1 1\\n\", \"4\\n1 6\\n\", \"5\\n2 1\\n\", \"3\\n1 7\\n\", \"3\\n1 19\\n\", \"3\\n1 3\\n\", \"3\\n1 5\\n\", \"4\\n1 3\\n\", \"3\\n1 17\\n\", \"7\\n8 1\\n\", \"13\\n1 4\\n\", \"10\\n1 10\\n\", \"6\\n7 1\\n\", \"4\\n1 1\\n\", \"13\\n1 5\\n\", \"10\\n1 6\\n\", \"8\\n1 4\\n\", \"15\\n1 16\\n\", \"14\\n2 1\\n\", \"5\\n1 7\\n\", \"23\\n2 6\\n\", \"23\\n1 10\\n\", \"12\\n4 3\\n\", \"9\\n1 10\\n\", \"4\\n1 1\\n\", \"10\\n3 1\\n\", \"5\\n10 1\\n\", \"15\\n7 1\\n\", \"8\\n1 3\\n\", \"10\\n3 1\\n\", \"3\\n1 5\\n\", \"7\\n12 1\\n\", \"3\\n1 17\\n\", \"3\\n1 2\\n\", \"33\\n1 3\\n\", \"9\\n2 4\\n\", \"6\\n7 1\\n\", \"8\\n4 1\\n\", \"3\\n1 4\\n\", \"7\\n2 1\\n\", \"4\\n1 6\\n\", \"5\\n2 1\\n\", \"3\\n1 7\\n\", \"3\\n1 19\\n\", \"14\\n2 1\\n\", \"8\\n7 2\\n\", \"13\\n1 5\\n\", \"13\\n1 3\\n\", \"5\\n1 7\\n\", \"23\\n2 6\\n\", \"23\\n1 10\\n\", \"9\\n1 10\\n\", \"4\\n2 1\\n\", \"14\\n7 1\\n\", \"10\\n3 1\\n\", \"3\\n1 5\\n\", \"6\\n7 1\\n\", \"5\\n10 1\\n\", \"8\\n1 3\\n\", \"10\\n3 1\\n\", \"3\\n1 5\\n\", \"7\\n12 1\\n\", \"3\\n1 17\\n\", \"10\\n3 1\\n\", \"33\\n1 3\\n\", \"9\\n2 4\\n\", \"6\\n7 1\\n\", \"8\\n4 1\\n\", \"3\\n2 1\\n\", \"1\\n2 6\\n\"]}", "dataset_type": "taco"} |
taco_7434 | deepcoder | Nastya owns too many arrays now, so she wants to delete the least important of them. However, she discovered that this array is magic! Nastya now knows that the array has the following properties:
In one second we can add an arbitrary (possibly negative) integer to all elements of the array that are not equal to zero. When all elements of the array become equal to zero, the array explodes.
Nastya is always busy, so she wants to explode the array as fast as possible. Compute the minimum time in which the array can be exploded.
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 10^5) — the size of the array.
The second line contains n integers a_1, a_2, ..., a_{n} ( - 10^5 ≤ a_{i} ≤ 10^5) — the elements of the array.
-----Output-----
Print a single integer — the minimum number of seconds needed to make all elements of the array equal to zero.
-----Examples-----
Input
5
1 1 1 1 1
Output
1
Input
3
2 0 -1
Output
2
Input
4
5 -6 -5 1
Output
4
-----Note-----
In the first example you can add - 1 to all non-zero elements in one second and make them equal to zero.
In the second example you can add - 2 on the first second, then the array becomes equal to [0, 0, - 3]. On the second second you can add 3 to the third (the only non-zero) element. | {"ground_truth": "{\"inputs\": [\"5\\n1 1 1 1 1\\n\", \"3\\n2 0 -1\\n\", \"4\\n5 -6 -5 1\\n\", \"1\\n0\\n\", \"2\\n21794 -79194\\n\", \"3\\n-63526 95085 -5239\\n\", \"3\\n0 53372 -20572\\n\", \"13\\n-2075 -32242 27034 -37618 -96962 82203 64846 48249 -71761 28908 -21222 -61370 46899\\n\", \"5\\n806 0 1308 1954 683\\n\", \"8\\n-26 0 -249 -289 -126 -206 288 -11\\n\", \"10\\n2 2 2 1 2 -1 0 2 -1 1\\n\", \"1\\n8\\n\", \"3\\n0 0 0\\n\", \"10\\n1 2 3 4 5 6 7 8 9 10\\n\", \"5\\n2 0 -1 0 0\\n\", \"2\\n0 0\\n\", \"5\\n0 0 0 0 0\\n\", \"2\\n1 0\\n\", \"2\\n-1 0\\n\", \"4\\n0 0 0 0\\n\", \"8\\n10 9 -1 0 0 3 2 3\\n\", \"5\\n5 0 1 2 3\\n\", \"3\\n1 1 0\\n\", \"1\\n-1\\n\", \"5\\n1 2 0 0 0\\n\", \"5\\n1 0 0 0 0\\n\", \"5\\n4 5 6 0 0\\n\", \"4\\n-1 0 0 1\\n\", \"5\\n3 0 0 4 5\\n\", \"3\\n0 0 2\\n\", \"3\\n1 0 0\\n\", \"4\\n0 0 0 4\\n\", \"5\\n-1 0 0 0 0\\n\", \"2\\n0 1\\n\", \"3\\n1 2 3\\n\", \"1\\n5\\n\", \"10\\n0 0 0 0 0 1 2 3 0 0\\n\", \"4\\n0 1 2 3\\n\", \"3\\n0 1 2\\n\", \"4\\n2 0 0 -1\\n\", \"10\\n1 2 3 4 5 6 7 8 9 10\\n\", \"4\\n2 0 0 -1\\n\", \"5\\n1 0 0 0 0\\n\", \"4\\n-1 0 0 1\\n\", \"3\\n0 1 2\\n\", \"3\\n0 0 2\\n\", \"5\\n4 5 6 0 0\\n\", \"5\\n1 2 0 0 0\\n\", \"4\\n0 1 2 3\\n\", \"2\\n0 1\\n\", \"5\\n0 0 0 0 0\\n\", \"5\\n5 0 1 2 3\\n\", \"5\\n2 0 -1 0 0\\n\", \"3\\n0 0 0\\n\", \"2\\n-1 0\\n\", \"2\\n0 0\\n\", \"1\\n0\\n\", \"3\\n-63526 95085 -5239\\n\", \"2\\n1 0\\n\", \"1\\n5\\n\", \"5\\n-1 0 0 0 0\\n\", \"10\\n0 0 0 0 0 1 2 3 0 0\\n\", \"5\\n3 0 0 4 5\\n\", \"5\\n806 0 1308 1954 683\\n\", \"13\\n-2075 -32242 27034 -37618 -96962 82203 64846 48249 -71761 28908 -21222 -61370 46899\\n\", \"1\\n-1\\n\", \"2\\n21794 -79194\\n\", \"4\\n0 0 0 4\\n\", \"8\\n-26 0 -249 -289 -126 -206 288 -11\\n\", \"1\\n8\\n\", \"3\\n1 2 3\\n\", \"3\\n1 0 0\\n\", \"10\\n2 2 2 1 2 -1 0 2 -1 1\\n\", \"8\\n10 9 -1 0 0 3 2 3\\n\", \"3\\n0 53372 -20572\\n\", \"4\\n0 0 0 0\\n\", \"3\\n1 1 0\\n\", \"10\\n2 2 3 4 5 6 7 8 9 10\\n\", \"4\\n4 0 0 -1\\n\", \"4\\n-1 0 0 0\\n\", \"5\\n2 0 1 2 3\\n\", \"5\\n806 1 1308 1954 683\\n\", \"13\\n-2075 -32242 27034 -37618 -96962 82203 64846 29532 -71761 28908 -21222 -61370 46899\\n\", \"8\\n-26 0 -249 -289 -126 -206 79 -11\\n\", \"5\\n2 0 1 4 3\\n\", \"10\\n2 2 3 4 1 6 1 8 9 10\\n\", \"5\\n1 -1 0 0 0\\n\", \"3\\n0 2 2\\n\", \"3\\n0 -1 2\\n\", \"5\\n4 5 4 0 0\\n\", \"5\\n1 3 0 0 0\\n\", \"4\\n0 2 2 3\\n\", \"2\\n1 1\\n\", \"5\\n0 -1 0 0 0\\n\", \"5\\n2 1 -1 0 0\\n\", \"3\\n0 0 -1\\n\", \"2\\n-2 0\\n\", \"2\\n0 -1\\n\", \"1\\n1\\n\", \"3\\n-63526 95085 -9386\\n\", \"2\\n1 -1\\n\", \"1\\n9\\n\", \"5\\n-2 0 0 0 0\\n\", \"10\\n0 0 0 0 0 1 2 2 0 0\\n\", \"5\\n3 0 0 6 5\\n\", \"1\\n-2\\n\", \"2\\n16913 -79194\\n\", \"4\\n0 0 1 4\\n\", \"1\\n3\\n\", \"3\\n0 2 3\\n\", \"3\\n1 0 1\\n\", \"10\\n2 2 2 1 2 0 0 2 -1 1\\n\", \"8\\n10 9 -1 0 0 0 2 3\\n\", \"3\\n0 53372 -28230\\n\", \"4\\n1 0 0 0\\n\", \"3\\n2 0 0\\n\", \"4\\n0 -6 -5 1\\n\", \"5\\n1 0 1 1 1\\n\", \"3\\n2 -1 -1\\n\", \"10\\n2 2 3 4 1 6 7 8 9 10\\n\", \"4\\n6 0 0 -1\\n\", \"5\\n1 -1 0 -1 0\\n\", \"4\\n0 0 0 -1\\n\", \"3\\n0 2 1\\n\", \"3\\n-1 -1 2\\n\", \"5\\n6 5 4 0 0\\n\", \"5\\n1 3 0 1 0\\n\", \"4\\n0 2 3 3\\n\", \"2\\n2 1\\n\", \"5\\n0 -1 0 1 0\\n\", \"5\\n4 1 -1 0 0\\n\", \"3\\n1 0 -1\\n\", \"2\\n-1 -1\\n\", \"2\\n0 -2\\n\", \"1\\n2\\n\", \"3\\n-63143 95085 -9386\\n\", \"2\\n1 -2\\n\", \"1\\n15\\n\", \"5\\n-2 0 -1 0 0\\n\", \"10\\n0 0 0 1 0 1 2 2 0 0\\n\", \"5\\n3 0 0 5 5\\n\", \"5\\n1006 0 1308 1954 683\\n\", \"13\\n-2075 -32242 27034 -37618 -96962 145894 64846 29532 -71761 28908 -21222 -61370 46899\\n\", \"1\\n-3\\n\", \"4\\n0 0 1 6\\n\", \"8\\n-17 0 -249 -289 -126 -206 79 -11\\n\", \"1\\n-4\\n\", \"3\\n0 0 3\\n\", \"3\\n1 0 2\\n\", \"10\\n2 2 2 1 2 0 -1 2 -1 1\\n\", \"8\\n10 12 -1 0 0 0 2 3\\n\", \"3\\n0 106114 -28230\\n\", \"4\\n1 1 0 0\\n\", \"3\\n4 0 0\\n\", \"4\\n0 -8 -5 1\\n\", \"5\\n1 0 1 1 2\\n\", \"3\\n2 -1 -2\\n\", \"4\\n6 0 1 -1\\n\", \"5\\n2 -1 0 -1 0\\n\", \"4\\n0 0 0 -2\\n\", \"3\\n0 1 1\\n\", \"3\\n0 -2 2\\n\", \"5\\n6 0 4 0 0\\n\", \"5\\n1 3 0 2 0\\n\", \"4\\n1 2 3 3\\n\", \"2\\n4 1\\n\", \"5\\n0 0 0 1 0\\n\", \"5\\n2 0 1 6 3\\n\", \"5\\n4 1 -1 -1 0\\n\", \"3\\n1 -1 -1\\n\", \"4\\n5 -6 -5 1\\n\", \"5\\n1 1 1 1 1\\n\", \"3\\n2 0 -1\\n\"], \"outputs\": [\"1\\n\", \"2\\n\", \"4\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"13\\n\", \"4\\n\", \"7\\n\", \"3\\n\", \"1\\n\", \"0\\n\", \"10\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"5\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"10\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"13\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"7\\n\", \"1\\n\", \"3\\n\", 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\"4\\n\", \"1\\n\", \"2\\n\"]}", "dataset_type": "taco"} |
taco_7435 | deepcoder | problem
There are $ N $ propositions, named $ 1, 2, \ cdots, N $, respectively. Also, $ M $ information about the propositions is given. The $ i $ th information is "$ a_i $$". Given in the form "b_i $", which means that $ a_i $ is $ b_i $. ("If" is a logical conditional and the transition law holds.) $ For each proposition $ i $ Output all propositions that have the same value as i $ in ascending order. However, proposition $ i $ and proposition $ i $ are always the same value. Proposition $ X $ and proposition $ Y $ have the same value as "$ if $ X $". It means "Y $" and "$ X $ if $ Y $".
output
On the $ i $ line, output all propositions that have the same value as the proposition $ i $, separated by blanks in ascending order. Also, output a line break at the end of each line.
Example
Input
5 2
1 2
2 1
Output
1 2
1 2
3
4
5 | {"ground_truth": "{\"inputs\": [\"5 2\\n1 2\\n2 2\", \"3 2\\n1 2\\n2 1\", \"3 2\\n1 2\\n3 1\", \"6 2\\n1 2\\n2 1\", \"9 2\\n1 2\\n2 4\", \"6 2\\n1 1\\n2 1\", \"17 2\\n1 2\\n2 4\", \"4 2\\n2 2\\n3 1\", \"26 2\\n2 2\\n4 4\", \"12 2\\n2 2\\n4 4\", \"1 0\\n2 2\\n1 1\", \"17 2\\n1 2\\n2 1\", \"7 1\\n2 1\\n3 0\", \"28 2\\n1 2\\n4 6\", \"18 2\\n1 3\\n2 2\", \"10 2\\n1 2\\n4 6\", \"48 0\\n4 3\\n8 4\", \"94 0\\n4 3\\n0 3\", \"178 0\\n4 3\\n0 3\", \"8 1\\n4 1\\n1 -1\", \"211 0\\n4 2\\n0 3\", \"9 2\\n1 2\\n2 1\", \"42 2\\n2 2\\n4 4\", \"2 0\\n1 3\\n1 1\", \"11 1\\n1 2\\n2 1\", \"2 2\\n1 2\\n2 1\", \"5 2\\n2 3\\n3 2\", \"20 2\\n1 1\\n4 6\", \"14 2\\n1 2\\n2 1\", \"39 0\\n2 2\\n8 0\", \"22 2\\n1 1\\n4 6\", \"24 0\\n4 5\\n8 4\", \"14 0\\n7 1\\n-1 0\", \"15 1\\n1 1\\n0 -1\", \"21 1\\n1 1\\n2 1\", \"38 1\\n2 2\\n6 4\", \"77 0\\n2 2\\n8 0\", \"75 0\\n5 2\\n0 3\", \"13 0\\n2 0\\n6 4\", \"65 0\\n5 2\\n0 3\", \"25 1\\n2 1\\n1 4\", \"40 0\\n4 0\\n14 3\", \"5 2\\n1 2\\n2 4\", \"5 2\\n2 2\\n2 1\", \"3 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\"1\\n2\\n3\\n4\\n5\\n\", \"1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n\", \"1\\n2\\n3\\n4\\n\", \"1\\n\", \"1\\n2\\n3\\n4\\n\", \"1\\n2\\n3\\n4\\n5\\n6\\n7\\n\", \"1\\n2\\n3\\n4\\n5\\n6\\n\", \"1 2\\n1 2\\n3\\n4\\n5\"]}", "dataset_type": "taco"} |
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