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(vec):
    if len(vec) == 0:
        return True
    h = 0
    for v in sorted(vec, reverse=True):
        if h + v[0] < 0:
            return False
        h += v[1]
    return True


def parse(brackets):
    m = 0
    f = 0
    for c in brackets:
        if c == "(":
            f += 1
        else:
            f -= 1
        if m > f:
            m = f
    return m, f


def main():
    N = int(input())
    ls = []
    rs = []
    tot = 0
    for _ in range(N):
        m, f = parse(input().strip())
        tot += f
        if f >= 0:
            ls.append([m, f])
        else:
            rs.append([m-f, -f])
    return tot == 0 and check(ls) and check(rs)


if __name__ == "__main__":
    print("Yes" if main() else "No")
