There are n students in a school class, the rating of the ii-th student on Codehorses is ai. You have to form a team consisting of k students (1≤k≤n) such that the ratings of all team members are distinct.
If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print kk distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.
Input
The first line contains two integers nn and kk (1≤k≤n≤100) — the number of students and the size of the team you have to form.
The second line contains nn integers a1,a2,…,an (1≤ai≤100), where aiai is the rating of ii-th student.
Output
If it is impossible to form a suitable team, print "NO" (without quotes). Otherwise print "YES", and then print kk distinct integers from 11 to nnwhich should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them.
Assume that the students are numbered from 1 to n.
You are given nn strings. Each string consists of lowercase English letters. Rearrange (reorder) the given strings in such a way that for every string, all strings that are placed before it are its substrings.
String aa is a substring of string b if it is possible to choose several consecutive letters in b in such a way that they form aa. For example, string "for" is contained as a substring in strings "codeforces", "for" and "therefore", but is not contained as a substring in strings "four", "fofo" and "rof".
Input
The first line contains an integer nn (1≤n≤100) — the number of strings.
The next nn lines contain the given strings. The number of letters in each string is from 1 to 100, inclusive. Each string consists of lowercase English letters.
Some strings might be equal.
Output
If it is impossible to reorder nn given strings in required order, print "NO" (without quotes).
Otherwise print "YES" (without quotes) and nn given strings in required order.
Examples
input
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5 a aba abacaba ba aba
output
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YES a ba aba aba abacaba
input
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5 a abacaba ba aba abab
output
Copy
NO
input
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3 qwerty qwerty qwerty
output
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YES qwerty qwerty qwerty
Note
In the second example you cannot reorder the strings because the string "abab" is not a substring of the string "abacaba".
You are given kk sequences of integers. The length of the ii-th sequence equals to nini.
You have to choose exactly two sequences ii and jj (i≠ji≠j) such that you can remove exactly one element in each of them in such a way that the sum of the changed sequence ii (its length will be equal to ni?1ni?1) equals to the sum of the changed sequence jj (its length will be equal to nj?1nj?1).
Note that it‘s required to remove exactly one element in each of the two chosen sequences.
Assume that the sum of the empty (of the length equals 00) sequence is 00.
Input
The first line contains an integer kk (2≤k≤2?105) — the number of sequences.
Then kk pairs of lines follow, each pair containing a sequence.
The first line in the ii-th pair contains one integer nini (1≤ni<2?105) — the length of the ii-th sequence. The second line of the ii-th pair contains a sequence of nini integers ai,1,ai,2,…,ai,niai,1,ai,2,…,ai,ni.
The elements of sequences are integer numbers from ?104?104 to 104104.
The sum of lengths of all given sequences don‘t exceed 2?105, i.e. n1+n2+?+nk≤2?105.
Output
If it is impossible to choose two sequences such that they satisfy given conditions, print "NO" (without quotes). Otherwise in the first line print "YES" (without quotes), in the second line — two integers ii, xx (1≤i≤k,1≤x≤ni1≤i≤k,1≤x≤ni), in the third line — two integers jj, yy (1≤j≤k,1≤y≤nj1≤j≤k,1≤y≤nj). It means that the sum of the elements of the ii-th sequence without the element with index xx equals to the sum of the elements of the jj-th sequence without the element with index yy.
Two chosen sequences must be distinct, i.e. i≠ji≠j. You can print them in any order.
If there are multiple possible answers, print any of them.
Examples
input
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2 5 2 3 1 3 2 6 1 1 2 2 2 1
output
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YES 2 6 1 2
input
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3 1 5 5 1 1 1 1 1 2 2 3
output
Copy
NO
input
Copy
4 6 2 2 2 2 2 2 5 2 2 2 2 2 3 2 2 2 5 2 2 2 2 2
output
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YES 2 2 4 1
Note
In the first example there are two sequences [2,3,1,3,2]and [1,1,2,2,2,1] You can remove the second element from the first sequence to get [2,1,3,2] and you can remove the sixth element from the second sequence to get [1,1,2,2,2][1,1,2,2,2]. The sums of the both resulting sequences equal to 88, i.e. the sums are equal.
There are nn distinct points on a coordinate line, the coordinate of ii-th point equals to xi. Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.
In other words, you have to choose the maximum possible number of points xi1,xi2,…,xim such that for each pair xijxij, xikxik it is true that |xij?xik|=2d where dd is some non-negative integer number (not necessarily the same for each pair of points).
Input
The first line contains one integer nn (1≤n≤2?105) — the number of points.
The second line contains nn pairwise distinct integers x1,x2,…,xn (?109≤xi≤109) — the coordinates of points.
Output
In the first line print mm — the maximum possible number of points in a subset that satisfies the conditions described above.
In the second line print mm integers — the coordinates of points in the subset you have chosen.
If there are multiple answers, print any of them.
Examples
input
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6 3 5 4 7 10 12
output
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3 7 3 5
input
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5 -1 2 5 8 11
output
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1 8
Note
In the first example the answer is [7,3,5]. Note, that |7?3|=4=22, |7?5|=2=21 and |3?5|=2=21. You can‘t find a subset having more points satisfying the required property.
You are given an integer nn from 11 to 1018 without leading zeroes.
In one move you can swap any two adjacent digits in the given number in such a way that the resulting number will not contain leading zeroes. In other words, after each move the number you have cannot contain any leading zeroes.
What is the minimum number of moves you have to make to obtain a number that is divisible by 25? Print -1 if it is impossible to obtain a number that is divisible by 25.
Input
The first line contains an integer nn (1≤n≤1018). It is guaranteed that the first (left) digit of the number nn is not a zero.
Output
If it is impossible to obtain a number that is divisible by 25, print -1. Otherwise print the minimum number of moves required to obtain such number.
Note that you can swap only adjacent digits in the given number.
Examples
input
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5071
output
Copy
4
input
Copy
705
output
Copy
1
input
Copy
1241367
output
Copy
-1
Note
In the first example one of the possible sequences of moves is 5071 →→ 5701 →→ 7501 →→ 7510 →→ 7150.