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 check(ar):
    h = 0
    for bottom, up in ar:
        if h + bottom < 0:
            return False
        h += up
    return True


if __name__ == "__main__":
    N = int(input())
    pos = []
    neg = []
    equal = 0
    for _ in range(N):
        cnt = 0
        bottom = 0
        for s in input():
            if s == "(":
                cnt += 1
            else:
                cnt -= 1
            bottom = min(bottom, cnt)
        equal += cnt
        if cnt >= 0:
            pos.append((bottom, cnt))
        else:
            cnt = -cnt
            bottom += cnt
            neg.append((bottom, cnt))

    pos.sort(reverse=True)
    neg.sort(reverse=True)
    if check(pos) and check(neg) and equal == 0:
        print("Yes")
    else:
        print("No")