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 bisect
n = int(input())
a = []; b = []; c = []
level = 0
for i in range(n):
    z = input()
    mm = 0; M = 0
    for x in z:
        if x == '(':
            M += 1
        elif x == ')':
            M -= 1
        mm = min(mm,M)
    if M > 0:
        a.append((mm,M))
    elif M == 0:
        b.append((mm,M))
    else:
        c.append((mm,M))

a.sort(reverse = True); b.sort(); c.sort()
d = a + b + c

for z in d:
    if level + z[0] >= 0:
        level += z[1]
    else:
        level = -1;break
if level == 0:
    print("Yes")
else:
    print("No")