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())
LR = [[0]*2 for i in range(N)]
for i in range(N):
    S = input()
    M = len(S)
    L = 0
    R = 0
    R0 = 0
    t = 0
    if S[0]==")":
        while t<M:
            if S[t]==")":
                R0+=1
                t+=1
            else:
                t+=1
                break
    while t<M:
        if S[t]=="(":
            t+=1
            L+=1
        else:
            t+=1
            R+=1
    if L>R:
        LR[i][0]=L-R
        LR[i][1]=R0
    if L<R:
        LR[i][0]=0
        LR[i][1]=R0+R-L
    if L==R:
        LR[i][0]=0
        LR[i][1]=R0

LP = 0
RP = 0
minLS = float('inf')
minRS = float('inf')
LS = 0
RS = 0
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:
        LS += L
        RS += R
        if LS < minLS:
            minLS = LS
        if RS < minRS:
            minRS = RS

if (minLS<RP)and(minRS<LP):
    print("Yes")
elif (LP==RP)and(LS==0)and(RS==0):
    print("Yes")
else:
    print("No")