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 ll long long int
ll mod=998244353;
ll mul(ll a, ll b)
{
	return ((a%mod)*(b%mod))%mod;
}
ll add(ll a, ll b)
{
	return ((a%mod)+(b%mod))%mod;
}
ll sub(ll a, ll b)
{
	return ((a%mod)-(b%mod)+mod)%mod;
}
bool sortbysec(const pair<int,int> &a,const pair<int,int> &b) 
{ 
    return (a.second < b.second); 
} 
int main() 
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	ll q;
	cin>>q;
	vector<pair<ll,ll>> v;
	while(q--)
	{
		string s;
		cin>>s;
		stack<char> st;
		for(ll i=0;i<s.size();i++)
		{
			if(st.size()==0)
			{
				st.push(s[i]);
				continue;
			}
			if(s[i]=='(')
			{
				st.push(s[i]);
			}
			else
			{
				if(st.top()=='(')
				{
					st.pop();
				}
				else
				{
					st.push(s[i]);
				}
			}
		}
		ll a=0,b=0;
		while(st.size())
		{
			if(st.top()=='(')
			{
				a++;
			}
			else
			{
				b++;
			}
			st.pop();
		}
		v.push_back(make_pair(b,a));
	}
	sort(v.begin(),v.end(),sortbysec);
	reverse(v.begin(),v.end());
	stack<char> st;
	for(ll i=0;i<v.size();i++)
	{
		
		for(ll j=0;j<v[i].first;j++)
		{
			if(st.size()==0)
			{
				st.push(')');
			}
			else
			{
				if(st.top()=='(')
				{
					st.pop();
				}
				else
				{
					st.push(')');
				}
			}
			
		}
		for(ll j=0;j<v[i].second;j++)
		{
			st.push('(');
		}
		
	}
	if(st.size()==0)
	{
		cout<<"Yes\n";
	}
	else
	{
		cout<<"No\n";
	}
	
}