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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
input = lambda: sys.stdin.readline().rstrip()

n = int(input())
s = []
for _ in range(n):
    s.append(input())

A = []

for i, j in enumerate(s):
    min_val = 0
    val = 10**10
   
    for k in j:
        if k == "(":
            val += 1
        else:
            val -= 1
        min_val = min(min_val, val)
    A.append([min_val, i])
A.sort()
A = A[::-1]
val = 0
for i, j in A:
    for k in list(s[j]):
        if k == "(":
            val += 1
        else:
            val -= 1
            if val < 0:
                print("No")
                sys.exit()
ans = "Yes" if val == 0 else "No"
print(ans)