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## A. Regular Bracket Sequence SOLUTION CodeForces

### Educational Codeforces Round 101 (Rated for Div. 2)

A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters + and 1 into this sequence. For example, sequences (())(), () and (()(())) are regular, while )(, (() and (()))( are not. Let’s call a regular bracket sequence “RBS”.

You are given a sequence s of n characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

You have to replace every character ? with either ) or ( (different characters ? can be replaced with different brackets). You cannot reorder the characters, remove them, insert other characters, and each ? must be replaced.

Determine if it is possible to obtain an RBS after these replacements.

Input

The first line contains one integer t (1≤t≤1000) — the number of test cases.

Each test case consists of one line containing s (2≤|s|≤100) — a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

Output

For each test case, print YES if it is possible to obtain a regular bracket sequence, or NO otherwise}.

You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).

Example

inputCopy

5

()

(?)

(??)

??()

)?(?

outputCopy

YES

NO

YES

YES

NO

Note

In the first test case, the sequence is already an RBS.

In the third test case, you can obtain an RBS as follows: ()() or (()).

In the fourth test case, you can obtain an RBS as follows: ()().

SOLUTION:

#include <bits/stdc++.h>

using namespace std;

#define ll long long int

int main()

{

int t;

cin>>t;

while(t–){

string s;

cin>>s;

int n=s.length();

if(n%2||s[0]==’)’||s[n-1]=='(‘) cout<<“NOn”;

else cout<<“YESn”;

}

}

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