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 resolve():
    def check(arr):
        height = 0
        for b, h in arr:
            if height+b < 0:
                return False
            height += h
        return True

    N = int(input())
    plus = []
    minus = []
    total = 0
    for _ in range(N):
        # 1つのパーツを処理
        S = input()
        cum = 0 # 累積和(最高地点)
        bottom = 0 # 最下地点
        for s in S:
            if s == "(":
                cum += 1
            else:
                cum -= 1
            bottom = min(bottom, cum)

        total += cum
        if cum > 0:
            plus.append((bottom, cum))
        else:
            minus.append((bottom-cum, -cum))

    plus.sort(reverse=True)
    minus.sort(reverse=True)

    if check(plus) and check(minus) and total == 0:
        print("Yes")
    else:
        print("No")

if __name__ == "__main__":
    resolve()
