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: Accepted)

N = int(input())
Up = []
Down = []
for _ in range(N):
    S = input()
    L = [0]
    mi = 0
    now = 0
    for __ in range(len(S)):
        if S[__] == '(':
            now += 1
        else:
            now -= 1
            mi = min(mi, now)
    if now > 0:
        Up.append((mi, now))
    else:
        Down.append((mi - now, mi, now))

Up.sort(reverse=True)
Down.sort()

now = 0
for i, j in Up:
    if now + i < 0:
        print('No')
        exit()
    else:
        now += j
for _, i, j in Down:
    if now + i < 0:
        print('No')
        exit()
    else:
        now += j
if now == 0:
    print('Yes')
else:
    print('No')