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)

def main():
    import queue
    import sys
    input = lambda : sys.stdin.readline().rstrip()
    sys.setrecursionlimit(max(1000, 10**9))



    n = int(input())
    minsum = [None] * n # (min, sum)
    for i in range(n):
        tmp = list(map(int, " ".join(input()).replace("(", "1").replace(")", "-1").split()))
        c = 0
        m = 0
        for item in tmp:
            c += item
            m = min(c, m)
        minsum[i] = (m, sum(tmp))
    minsum.sort()

    if sum(item[1] for item in minsum)!=0:
        print("No")
    else:
        minsum1 = [item for item in minsum if item[1]>=0]
        minsum2 = [(item[0]-item[1], -item[1]) for item in minsum if item[1]<0]
        c = 0
        for m,s in minsum1[::-1]:
            if c+m>=0:
                c += s
            else:
                print("No")
                return
        c = 0
        for m,s in minsum2[::-1]:
            if c+m>=0:
                c+=s
            else:
                print("No")
                return
        print("Yes")
main()