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)

N=int(input())
L=[]
Sum=0
F=0
for i in range(N):
    s=input()
    Min=0
    cnt=0
    for j in range(len(s)):
        if s[j]=="(":
            cnt+=1
        else:
            cnt-=1
            if Min>=cnt:
                Min=cnt
    if cnt>=0:
        L.append([-Min,-cnt])
    else:
        if Min==cnt:
            F=1
    Sum+=cnt
if Sum!=0:
    print("No")
else:
    L.sort()
    Sum=0
    for Min,cnt in L:
        if Sum-Min>=0:
            Sum-=cnt
        else:
            print("No")
            exit()
    if F==1:
        print("Yes")
    else:
        print("No")
    #print(L)