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: Runtime Error)

import sys
N = int(f.input())
S = [str(f.input()) for _ in range(N)]

plus_stock = []
minus_stock = []
for i, row in enumerate(S):
    lowest = 0
    now = 0
    for j,char in enumerate(row):
        if char == "(":
            now+=1
        elif char == ")":
            now-=1 
        if now < lowest:
            lowest = now
    if now >= 0:
        plus_stock.append([now, lowest])
    else:
        minus_stock.append([-now, lowest - now])
plus_stock  = sorted(plus_stock, key = lambda x:x[1])
minus_stock = sorted(minus_stock, key = lambda x:x[1])

now = 0

for i in range(len(plus_stock)):
    if now + plus_stock[i][1] < 0:
        print("No")
        sys.exit()
    else:
        now = now+plus_stock[i][0]
last = now
now = 0
for i in range(len(minus_stock)):
    if now + minus_stock[i][1] < 0:
        print("No")
        sys.exit()
    else:
        now = now+minus_stock[i][0]
if last == now:
    print("Yes")
else:
    print("No")