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
#!python3

def LI():
    return list(map(int, input().split()))

# input
N = int(input())
S = [input() for _ in range(N)]


def judge(v):
    x = 0
    for b, l in v:
        if x + b < 0:
            return False
        x += l
    return True


def main():
    pl, ml = [], []
    t = 0
    for i in range(N):
        l = 0
        b = 0
        for s in S[i]:
            if s == "(":
                l += 1
            else:
                l -= 1
                b = min(b, l)
        t += l
        if l > 0:
            pl.append((b, l))
        else:
            ml.append((b - l, -l))

    pl.sort(reverse=True)
    ml.sort(reverse=True)

    if judge(pl) and judge(ml) and t == 0:
        print("Yes")
    else:
        print("No")


if __name__ == "__main__":
    main()
