Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int M = 1e6 + 5;
int n, bal[M];

bool cmp(const int &a, const int &b)
{
	return bal[a] > bal[b];
}

bool check(string ans)
{
	int cur = 0;
	for(auto &c : ans)
	{
		cur += (c == '(' ? 1 : -1);
		if(cur < 0)
			return 0;
	}
	return cur == 0;
}
 
int32_t main() 
{
	ios_base::sync_with_stdio(0);	cin.tie(0);	cout.tie(0);
	cin >> n;
	vector <string> s(n);
	vector <int> v(n);
	for(int i = 0; i < n; i++)
	{
		cin >> s[i];
		v[i] = i;
		for(auto &c : s[i])
			bal[i] += (c == '(' ? 1 : -1);
	}
	sort(v.begin(), v.end(), cmp);
	string ans = "";
	for(auto &i : v)
		ans += s[i];
	cout << (check(ans) ? "Yes" : "No"); 
    	return 0;
}