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)

import re

n = int(input())
s = set()
for i in range(n):
    ss = input().rstrip()
    ns = len(ss)
    while True:
        ss = ss.replace('()', '')
        nns = len(ss)
        if nns == ns:
            break
        ns = nns
    if ss:
        s.add(ss)

ss = ''.join(sorted(list(s)))
ns = len(ss)
while True:
    ss = ss.replace('()', '')
    nns = len(ss)
    if nns == ns:
        break
    ns = nns
if len(ss) == 0:
    print('Yes')
else:
    print('No')