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)

# F - Bracket Sequencing

N = int(input())
L = []
for _ in range(N):
    S = list(str(input()))
    d = 0
    min_d = 0
    for s in S:
        if s == '(':
            d += 1
        else:
            d -= 1
            min_d = min(min_d, d)
    L.append((d, min_d))

L.sort(key=lambda x: x[1], reverse=True)
L.sort(key=lambda x: x[0], reverse=True)

ans = 'Yes'
now = 0
for d, min_d in L:
    if now + min_d < 0:
        ans = 'No'
        break
    else:
        now += d

if now != 0:
    ans = 'No'

print(ans)