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 I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    mod=10**9+7
    N=I()
    on=0
    L=[]

    for i in range(N):
        s=input()
        close=0
        openn=0
        for ch in s:
            if ch==")":
                if openn==0:
                    close+=1
                else:
                    openn-=1
            else:
                openn+=1
        if close==0:
            on+=openn
        else:
            L.append((close,-1*openn))
    L.sort()
    flag=1
    
    #print(on)
    
    for co in L:
        cc=co[0]
        oo=co[1]
        #print(cc,oo)
        on-=cc
        if on<0:
            flag=0
            break
        on-=oo
        
    #print(on)    
    
    if on!=0:
        flag=0
        
    if flag==1:
        print("Yes")
    else:
        print("No")
        
        
    
      
        
    

main()