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 Python (3.8.2) (judge verdict: Wrong Answer)

from sys import stdin

def checker(x):
    l = x.count('(', 1, -1)
    r = len(x[1:-1]) - l
    if l != r: return 0

    sum = 0
    for c in x:
        if c == '(':
            sum = sum + 1
        else:
            sum = sum - 1
        if sum < 0: return 0
    if sum != 0 : return 0

    return 1

def main():
    readline = stdin.readline
    n = int(readline())
    s = tuple(readline().strip() for _ in range(n))

    sorted_s = sorted(s)
    jud = checker(''.join(sorted_s))

    if jud == 1:
        print('Yes')
    else:
        print('No')
    return

if __name__ == '__main__':
    main()