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<bits/stdc++.h>
using namespace std;
int n,res=0,sum=0;
string s;
vector<pair<int,int> >v;
bool cmp(pair<int,int>p1,pair<int,int>p2) {return min(p1.second,p1.first+p2.second)>min(p2.second,p2.first+p1.second);}
int main()
{
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>s;
        int cnt=0,mn=0;
        for(char c:s) c=='('?cnt++:cnt--,mn=min(mn,cnt);
        v.emplace_back(cnt,mn);
        sum+=cnt;
    }
    if(sum!=0) {puts("No");exit(0);}
    sort(v.begin(),v.end(),cmp);
    for(pair<int,int>p:v){
        if(res<-p.second){
            puts("No");exit(0);
        }
        res+=p.first;
    }
    puts("Yes");
    return 0;
}