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)

N = int(input())
LR = [[0]*2 for i in range(N)]
for i in range(N):
    S = input()
    M = len(S)
    t = 0
    Life = 0
    R = 0
    while t<M:
        if S[t]=="(":
            Life += 1
        elif S[t]==")":
            if Life>=1:
                Life += -1
            else:
                R+=1
        t+=1
    LR[i][0] = Life #L
    LR[i][1] = R    # R

LP = 0
RP = 0
X = []
for i in range(N):
    L = LR[i][0]
    R = LR[i][1]
    if (L==0)and(R==0):
        continue
    elif L==0:
        RP += R
    elif R==0:
        LP += L
    else:
        X.append([L,R,L-R])

X.sort(key=lambda x:x[2],reverse=True)

Life = LP
if Life==0:
    if (RP==0)and(len(X)==0):
        print("Yes")
    else:
        print("No")
else:
    flag = 1
    for i in range(len(X)):
        Life += -1*X[i][1]
        if (Life<0)and(X[1]-X[2]<0):
            flag=0
        Life += X[i][0]
    if flag==0:
        print("No")
    elif Life==RP:
        print("Yes")
    else:
        print("No")