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)

import sys
n=int(input())
lrp=[]
lrm=[]
def g(s):
    i = 0
    l = [0]
    for j in s:
        if j =="(":
            i += 1
        else:
            i -= 1
        l.append(i)
    return min(l),max(l)
for _ in range(n):
    s = input()
    l = s.count("(")
    r = len(s) - l
    mi,ma =g(s)
    if l>r:
        lrp.append((l,r))
    else:
        lrm.append((l,r))
    #lr.append((mi,ma,l,r))
    
lrp.sort(key=lambda x:x[0])
lrm.sort(key=lambda x:-x[1])
lr=lrp+lrm
num = 0
for right,left in lr:
    num -= right
    if(num < 0):
        print('No')
        sys.exit()
    num += left
if(num==0):
    print('Yes')
else:
    print('No')