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: Runtime Error)

#include<stdio.h>
#include<string.h>
int main()
{
    int i,n,j,c=0,d=0,l;
    char s[100000];
    char a[100000];
    scanf("%d\n",&n);
    for(i=0;i<n;i++)
    {
        scanf("%s\n",a);
        strcat(s,a);
    }
    //printf("%s",s);
    //l=strlen(s);
    for(j=0;s[j]!='\0';j++)
    {
        if(s[j]=='(')
        {
            c++;
        }
        else if(s[j]==')')
        {
            d++;
        }
    }
    if(c==d)
    {
        printf("Yes");
    }
    else
    {
        printf("No");
    }
}