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 sys

readline = sys.stdin.readline
readlines = sys.stdin.readlines
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
prn = lambda x: print(*x, sep='\n')

n = ni()
l = [ns() for _ in range(n)]
gu = list()
gd = list()
c = 0
for i in range(n):
    s = l[i]
    t = 0
    m = 0
    for x in s:
        if x == '(':
            t += 1
        else:
            t -= 1
            if m > t:
                m = t
    c += t
    if t > 0:
        gu.append((m, -t))
    else:
        gd.append((m, -t))
if c != 0:
    print('No')
    exit(0)
gu.sort()
gd.sort()
cur = 0
for m, t in gu + gd:
    if cur + m < 0:
        print('No')
        exit(0)
    cur -= t
print('Yes')