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
import sys
input = sys.stdin.readline
def main():
    N = int( input())
    S = [input().strip() for _ in range(N)]
    Up = []
    Down = []
    for s in S:
        now = 0
        m = 0
        for t in s:
            if t == "(":
                now += 1
            else:
                now -= 1
            if now < m:
                m = now
            # print(t, now)
        if now >= 0:
            Up.append((m,now))
        else:
            Down.append((m-now,-now))
    up = 0
    Up.sort(reverse=True)
    for m, inc in Up:
        if up+m < 0:
            print("No")
            return
        up += inc
    
    down = 0
    Down.sort(reverse=True)
    # print(Up, Down)
    for m, dec in Down:
        if down+m < 0:
            print("No")
            return
        down += dec
    if up != down:
        print("No")
        return
    print("Yes")
    
if __name__ == '__main__':
    main()
