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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
flag = 0
ML = []
MM = []
MR = []
L = 0
R = 0
for _ in range(n):
    s = input()
    saisho = 0
    cur = 0
    for w in s:
        if w == "(":
            cur += 1
        else:
            cur -= 1
        saisho = min(saisho, cur)
    if saisho == 0:
        if cur > 0:
            L += cur
        elif cur < 0:
            R += -cur
    else:
        if cur > 0:
            ML.append((saisho, cur))
        elif cur < 0:
            MR.append((saisho, cur))
        else:
            MM.append((saisho, cur))
ML.sort(reverse=True)
MR.sort()
now = L
for saisho, delta in ML:
    if now + saisho < 0:
        flag = 1
    now += delta
for saisho, delta in MM:
    if now + saisho < 0:
        flag = 1
    now += delta
for saisho, delta in MR:
    if now + saisho < 0:
        flag = 1
    now += delta

if now != R:
    flag = 1
if flag:
    print("No")
else:
    print("Yes")