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():
    n = int(input())
    up = []
    down = []
    for _ in range(n):
        height = 0
        m = 0
        for si in input():
            if si == "(":
                height += 1
            else:
                height -= 1
                m = min(m, height)
        if height >= 0:
            up.append([m, height])
        else:
            down.append([m-height, -height])
    up.sort(reverse=True)
    down.sort(reverse=True)
    if sum([i for _, i in up]) - sum([i for _, i in down]) != 0:
        print("No")
        return
    h = 0
    for mi, hi in up:
        if h+mi < 0:
            print("No")
            return
        h += hi
    h = 0
    for mi, hi in down:
        if h+mi < 0:
            print("No")
            return
        h += hi
    print("Yes")
    return
            

if __name__ == "__main__":
    main()