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 to_lines(s):
    h = 0
    b = 0
    for c in s:
        if c == '(':
            h += 1
        else:
            h -= 1
        b = min([b, h])
    return (b, h)


def check(lines):
    h = 0
    for line in lines:
        if h + line[0] < 0:
            return False
        h += line[1]
    return True


def main():
    N = int(input())
    up_lines = list()
    down_lines = list()
    total = 0
    for _ in range(N):
        line = to_lines(input())
        total += line[1]
        if line[1] >= 0:
            up_lines.append(line)
        else:
            inv_line = (line[0] - line[1], -line[1])
            down_lines.append(inv_line)
    up_lines.sort(key=lambda x: x[0], reverse=True)
    down_lines.sort(key=lambda x: x[0], reverse=True)
    if total == 0 and check(up_lines) and check(down_lines):
        print('Yes')
    else:
        print('No')


if __name__ == '__main__':
    main()