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 collections import deque

N = int(input())

right = False
left = False

right_sum = 0
left_sum = 0

for i in range(N):
    S = input()
    br_q = deque()
    for s_index, c in enumerate(S):
        br_is_right = (c == "(")
        if len(br_q) == 0:
            br_q.append(br_is_right)
        else:
            if br_q[-1] and not br_is_right:
                br_q.pop()
            else:
                br_q.append(br_is_right)
    right_count = 0
    left_count = 0
    for is_right in br_q:
        if is_right:
            right_count += 1
        else:
            left_count += 1
    right_sum += right_count
    left_sum += left_count
    if right_count == 0 and not left:
        left = True
    elif left_count == 0:
        right = True

if right and left and right_sum == left_sum:
    print("Yes")
else:
    print("No")