desc
stringclasses 10
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stringclasses 10
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Problem description.
Vipul is a hardworking super-hero who maintains the bracket ratio of all the strings in the world. Recently he indulged himself in saving the string population so much that he lost his ability for checking brackets (luckily, not permanently ).Being his super-hero friend help him in his time of hardship.
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single string S denoting the string to be checked.
Output
For each test case, output a single line printing "YES" or "NO" (without " " and in uppercase only) , denoting if the brackets in the given string is balanced or not .
Constraints
1 ≤ T ≤ 10
1 ≤ length of S ≤ 60
Example
Input:
3
((()))
(())()
()(()
Output:
YES
YES
NO
Explanation
Example is self-explanatory. | solution_0 |
The Chef likes to stay in touch with his staff. So, the Chef, the head server, and the sous-chef all carry two-way transceivers so they can stay in constant contact. Of course, these transceivers have a limited range so if two are too far apart, they cannot communicate directly.
The Chef invested in top-of-the-line transceivers which have a few advanced features. One is that even if two people cannot talk directly because they are out of range, if there is another transceiver that is close enough to both, then the two transceivers can still communicate with each other using the third transceiver as an intermediate device.
There has been a minor emergency in the Chef's restaurant
and he needs to communicate with both the head server and the sous-chef right away. Help the Chef determine if it is possible for all three people to communicate with each other, even if two must communicate through the third because they are too far apart.
Input
The first line contains a single positive integer T ≤ 100 indicating the number of test cases to follow. The first line of each test case contains a positive integer R ≤ 1,000 indicating that two transceivers can communicate directly without an intermediate transceiver if they are at most R meters away from each other. The remaining three lines of the test case describe the current locations of the Chef, the head server, and the sous-chef, respectively. Each such line contains two integers X,Y (at most 10,000 in absolute value) indicating that the respective person is located at position X,Y.
Output
For each test case you are to output a single line containing a single string. If it is possible for all three to communicate then you should output "yes". Otherwise, you should output "no".
To be clear, we say that two transceivers are close enough to communicate directly if the length of the straight line connecting their X,Y coordinates is at most R.
Example
Input:
3
1
0 1
0 0
1 0
2
0 1
0 0
1 0
2
0 0
0 2
2 1
Output:
yes
yes
no | solution_1 |
Frank explained its friend Felman the algorithm of Euclides to calculate the GCD
of two numbers. Then Felman implements it algorithm
int gcd(int a, int b)
{
if (b==0)
return a;
else
return gcd(b,a%b);
}
and it proposes to Frank that makes it
but with a little integer and another integer that has up to 250 digits.
Your task is to help Frank programming an efficient code for the challenge of Felman.
Input
The first line of the input file contains a number representing the number of lines to follow.
Each line consists of two number A and B (0 ≤ A ≤ 40000 and A ≤ B < 10^250).
Output
Print for each pair (A,B) in the input one integer representing the GCD of A and B.
Example
Input:
2
2 6
10 11
Output:
2
1 | solution_2 |
A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7.
The Little Elephant calls some string T of the length M balanced if there exists at least one integer X (1 ≤ X ≤ M) such that the number of digits 4 in the substring T[1, X - 1] is equal to the number of digits 7 in the substring T[X, M]. For example, the string S = 7477447 is balanced since S[1, 4] = 7477 has 1 digit 4 and S[5, 7] = 447 has 1 digit 7. On the other hand, one can verify that the string S = 7 is not balanced.
The Little Elephant has the string S of the length N. He wants to know the number of such pairs of integers (L; R) that 1 ≤ L ≤ R ≤ N and the substring S[L, R] is balanced. Help him to find this number.
Notes.
Let S be some lucky string. Then
|S| denotes the length of the string S;
S[i] (1 ≤ i ≤ |S|) denotes the i^th character of S (the numeration of characters starts from 1);
S[L, R] (1 ≤ L ≤ R ≤ |S|) denotes the string with the following sequence of characters: S[L], S[L + 1], ..., S[R], and is called a substring of S. For L > R we mean by S[L, R] an empty string.
Input
The first line of the input file contains a single integer T, the number of test cases. Each of the following T lines contains one string, the string S for the corresponding test case. The input file does not contain any whitespaces.
Output
For each test case output a single line containing the answer for this test case.
Constraints
1 ≤ T ≤ 10
1 ≤ |S| ≤ 100000
S consists only of the lucky digits 4 and 7.
Example
Input:
4
47
74
477
4747477
Output:
2
2
3
23
Explanation
In the first test case balance substrings are S[1, 1] = 4 and S[1, 2] = 47.
In the second test case balance substrings are S[2, 2] = 4 and S[1, 2] = 74.
Unfortunately, we can't provide you with the explanations of the third and the fourth test cases. You should figure it out by yourself. Please, don't ask about this in comments. | solution_3 |
Given a string s. Can you make it a palindrome by deleting exactly one character? Note that size of the string after deletion would be one less than it was before.
Input
First line of the input contains a single integer T denoting number of test cases.
For each test case, you are given a single line containing string s.
Output
For each test case, print YES or NO depending on the answer of the problem.
Constraints
Example
Input:
4
aaa
abc
abdbca
abba
Output:
YES
NO
YES
YES
Explanation
Example case 1. Delete any one 'a', resulting string is "aa" which is a palindrome.
Example case 2. It is not possible to delete exactly one character and having a palindrome.
Example case 3. Delete 'c', resulting string is "abdba" which is a palindrome.
Example case 4. Delete 'b', resulting string is "aba" which is a palindrome. | solution_4 |
An established group of scientists are working on finding solution to NP hard problems. They claim Subset Sum as an NP-hard problem. The problem is to determine whether there exists a subset of a given set S whose sum is a given number K.
You are a computer engineer and you claim to solve this problem given that all numbers in the set are non-negative. Given a set S of size N of non-negative integers, find whether there exists a subset whose sum is K.
Input
First line of input contains T, the number of test cases. T test cases follow.
Each test case contains 2 lines. First line contains two integers N and K. Next line contains N space separated non-negative integers (each less than 100000).
0 < T < 1000
0 < N < 1000
0 < K < 1000
Output
Output T lines, one for each test case. Every line should be either 0 or 1 depending on whether such a subset exists or not.
Example
Input:
2
5 10
3 4 6 1 9
3 2
1 3 4
Output:
1
0 | solution_5 |
You are given an array of n positive integers a_1, a_2, ..., a_n. You can perform the following operation any number of times: select several distinct indices i_1, i_2, ..., i_k (1 ≤ i_j ≤ n) and move the number standing at the position i_1 to the position i_2, the number at the position i_2 to the position i_3, ..., the number at the position i_k to the position i_1. In other words, the operation cyclically shifts elements: i_1 → i_2 → … i_k → i_1.
For example, if you have n=4, an array a_1=10, a_2=20, a_3=30, a_4=40, and you choose three indices i_1=2, i_2=1, i_3=4, then the resulting array would become a_1=20, a_2=40, a_3=30, a_4=10.
Your goal is to make the array sorted in non-decreasing order with the minimum number of operations. The additional constraint is that the sum of cycle lengths over all operations should be less than or equal to a number s. If it's impossible to sort the array while satisfying that constraint, your solution should report that as well.
Input
The first line of the input contains two integers n and s (1 ≤ n ≤ 200 000, 0 ≤ s ≤ 200 000)—the number of elements in the array and the upper bound on the sum of cycle lengths.
The next line contains n integers a_1, a_2, ..., a_n—elements of the array (1 ≤ a_i ≤ 10^9).
Output
If it's impossible to sort the array using cycles of total length not exceeding s, print a single number "-1" (quotes for clarity).
Otherwise, print a single number q— the minimum number of operations required to sort the array.
On the next 2 ⋅ q lines print descriptions of operations in the order they are applied to the array. The description of i-th operation begins with a single line containing one integer k (1 ≤ k ≤ n)—the length of the cycle (that is, the number of selected indices). The next line should contain k distinct integers i_1, i_2, ..., i_k (1 ≤ i_j ≤ n)—the indices of the cycle.
The sum of lengths of these cycles should be less than or equal to s, and the array should be sorted after applying these q operations.
If there are several possible answers with the optimal q, print any of them.
Examples
Input
5 5
3 2 3 1 1
Output
1
5
1 4 2 3 5
Input
4 3
2 1 4 3
Output
-1
Input
2 0
2 2
Output
0
Note
In the first example, it's also possible to sort the array with two operations of total length 5: first apply the cycle 1 → 4 → 1 (of length 2), then apply the cycle 2 → 3 → 5 → 2 (of length 3). However, it would be wrong answer as you're asked to use the minimal possible number of operations, which is 1 in that case.
In the second example, it's possible to the sort the array with two cycles of total length 4 (1 → 2 → 1 and 3 → 4 → 3). However, it's impossible to achieve the same using shorter cycles, which is required by s=3.
In the third example, the array is already sorted, so no operations are needed. Total length of empty set of cycles is considered to be zero. | solution_6 |
There are n persons who initially don't know each other. On each morning, two of them, who were not friends before, become friends.
We want to plan a trip for every evening of m days. On each trip, you have to select a group of people that will go on the trip. For every person, one of the following should hold:
* Either this person does not go on the trip,
* Or at least k of his friends also go on the trip.
Note that the friendship is not transitive. That is, if a and b are friends and b and c are friends, it does not necessarily imply that a and c are friends.
For each day, find the maximum number of people that can go on the trip on that day.
Input
The first line contains three integers n, m, and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 2 ⋅ 10^5, 1 ≤ k < n) — the number of people, the number of days and the number of friends each person on the trip should have in the group.
The i-th (1 ≤ i ≤ m) of the next m lines contains two integers x and y (1≤ x, y≤ n, x≠ y), meaning that persons x and y become friends on the morning of day i. It is guaranteed that x and y were not friends before.
Output
Print exactly m lines, where the i-th of them (1≤ i≤ m) contains the maximum number of people that can go on the trip on the evening of the day i.
Examples
Input
4 4 2
2 3
1 2
1 3
1 4
Output
0
0
3
3
Input
5 8 2
2 1
4 2
5 4
5 2
4 3
5 1
4 1
3 2
Output
0
0
0
3
3
4
4
5
Input
5 7 2
1 5
3 2
2 5
3 4
1 2
5 3
1 3
Output
0
0
0
0
3
4
4
Note
In the first example,
* 1,2,3 can go on day 3 and 4.
In the second example,
* 2,4,5 can go on day 4 and 5.
* 1,2,4,5 can go on day 6 and 7.
* 1,2,3,4,5 can go on day 8.
In the third example,
* 1,2,5 can go on day 5.
* 1,2,3,5 can go on day 6 and 7. | solution_7 |
Let's call a string a phone number if it has length 11 and fits the pattern "8xxxxxxxxxx", where each "x" is replaced by a digit.
For example, "80123456789" and "80000000000" are phone numbers, while "8012345678" and "79000000000" are not.
You have n cards with digits, and you want to use them to make as many phone numbers as possible. Each card must be used in at most one phone number, and you don't have to use all cards. The phone numbers do not necessarily have to be distinct.
Input
The first line contains an integer n — the number of cards with digits that you have (1 ≤ n ≤ 100).
The second line contains a string of n digits (characters "0", "1", ..., "9") s_1, s_2, …, s_n. The string will not contain any other characters, such as leading or trailing spaces.
Output
If at least one phone number can be made from these cards, output the maximum number of phone numbers that can be made. Otherwise, output 0.
Examples
Input
11
00000000008
Output
1
Input
22
0011223344556677889988
Output
2
Input
11
31415926535
Output
0
Note
In the first example, one phone number, "8000000000", can be made from these cards.
In the second example, you can make two phone numbers from the cards, for example, "80123456789" and "80123456789".
In the third example you can't make any phone number from the given cards. | solution_8 |
Chouti thought about his very first days in competitive programming. When he had just learned to write merge sort, he thought that the merge sort is too slow, so he restricted the maximum depth of recursion and modified the merge sort to the following:
<image>
Chouti found his idea dumb since obviously, this "merge sort" sometimes cannot sort the array correctly. However, Chouti is now starting to think of how good this "merge sort" is. Particularly, Chouti wants to know for a random permutation a of 1, 2, …, n the expected number of inversions after calling MergeSort(a, 1, n, k).
It can be proved that the expected number is rational. For the given prime q, suppose the answer can be denoted by u/d where gcd(u,d)=1, you need to output an integer r satisfying 0 ≤ r<q and rd ≡ u \pmod q. It can be proved that such r exists and is unique.
Input
The first and only line contains three integers n, k, q (1 ≤ n, k ≤ 10^5, 10^8 ≤ q ≤ 10^9, q is a prime).
Output
The first and only line contains an integer r.
Examples
Input
3 1 998244353
Output
499122178
Input
3 2 998244353
Output
665496236
Input
9 3 998244353
Output
449209967
Input
9 4 998244353
Output
665496237
Note
In the first example, all possible permutations are [1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1].
With k=1, MergeSort(a, 1, n, k) will only return the original permutation. Thus the answer is 9/6=3/2, and you should output 499122178 because 499122178 × 2 ≡ 3 \pmod {998244353}.
In the second example, all possible permutations are [1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1] and the corresponding outputs of MergeSort(a, 1, n, k) are [1,2,3],[1,2,3],[2,1,3],[1,2,3],[2,3,1],[1,3,2] respectively. Thus the answer is 4/6=2/3, and you should output 665496236 because 665496236 × 3 ≡ 2 \pmod {998244353}. | solution_9 |