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 = []
#[c,d]c=right d=left
for i in range(n):
    s = list(input())
    c = 0
    d = 0
    for j in range(len(s)):
        if s[j] == "(":
            c += 1
        else:
            if c > 0:
                c -= 1
            else:
                d += 1
    l.append([c,d])
key = [0,0,0]
ac = 0
ad = 0
for i in range(n):
    c,d = l[i]
    if c == 0:
        if d == 0:
            key[2] += 1
        else:
            key[0] += 1
    else:
        if d == 0:
            key[1] += 1
    ac += c
    ad += d
if ac == ad:
    if key[0] > 0 and key[1] > 0:
        print("Yes")
    else:
        print("No")
else:
    print("No")