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

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. 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`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

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


Output

Yes


Input

3
(((
)
)


Output

No
#include <iostream>
#include <algorithm>
using namespace std;
pair <int,int> a[1000005];
inline bool cmp(pair <int,int> x,pair <int,int> y)
{
	if(x.second-x.first>=0&&y.second-y.first<0) return 1;
	if(x.second-x.first<0&&y.second-y.first>=0) return 0;
	if(x.second-x.first>=0) return x.first<y.first;
	else return -x.first+x.second-y.first>-y.first+y.second-x.first;
}
int main(int argc, char** argv) {
	int n;
	cin >> n;
	for(int i=1;i<=n;i++)
	{
		string s;
		cin >> s;
		int l=0,r=0;
		for(auto x:s)
		{
			if(x=='(') ++l;
			else if(l) --l;
			else ++r;
		}
		a[i]={r,l};
	//	cout << a[i].first << " " << a[i].second << "\n";
	}
	sort(a+1,a+n+1,cmp);
	int now=0;
	for(int i=1;i<=n;i++)
	{
		now-=a[i].first;
		if(now<0)
		{
			puts("No");
			return 0;
		}
		now+=a[i].second;
	}
	if(now) puts("No");
	else puts("Yes");
	return 0;
}