p02686 AtCoder Beginner Contest 167 - Bracket Sequencing
A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. 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`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

4
((()))
((((((
))))))
()()()


Output

Yes


Input

3
(((
)
)


Output

No
```python
import sys
input = sys.stdin.readline

N = int(input())
S = [input()[:-1] for _ in range(N)]
rl1, rl2 = [], []

for Si in S:
    l, r = 0, 0
    
    for i in range(len(Si)):
        if Si[i]=='(':
            l += 1
        else:
            if l==0:
                r += 1
            else:
                l -= 1
    
    if l-r>=0:
        rl1.append((r, l))
    else:
        rl2.append((r, l))
    
rl1.sort(key=lambda t: t[0])
rl2.sort(key=lambda t: t[1], reverse=True)
rl3 = rl1+rl2
bal = 0

for r, l in rl3:
    bal -= r
    
    if bal<0:
        print('No')
        exit()
    
    bal += l

if bal==0:
    print('Yes')
else:
    print('No')
```