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
def main():
    import sys
    input = sys.stdin.readline
    N = int(input())
    plus = []
    minus = []
    total = 0
    for _ in range(N):
        s = input().strip()
        h = 0
        bottom = 0
        for ss in s:
            if ss == "(":
                h += 1
            else:
                h -= 1
                bottom = min(bottom, h)
        total += h
        if h > 0:
            plus.append((bottom, h))
        else:
            minus.append((bottom-h, -h))
    if total != 0:
        print("No")
        sys.exit()
    plus.sort(reverse=True)
    minus.sort(reverse=True)
    height = 0
    for b, h in plus:
        if height + b < 0:
            print("No")
            sys.exit()
        height += h
    height = 0
    for b, h in minus:
        if height + b < 0:
            print("No")
            sys.exit()
        height += h
    print("Yes")
        


if __name__ == '__main__':
    main()