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():
    import sys
    from collections import deque
    sys.setrecursionlimit(10**6)
    input = sys.stdin.readline
    N = int(input())
    pq = deque([])
    mq = deque([])
    for n in range(N):
        s = input().strip()
        mini = 0
        dst = 0
        for ss in [1 if ss == '(' else -1 for ss in s]:
            dst += ss
            mini = min(dst, mini)
        
        if dst >= 0:
            pq.append((mini, dst))
        elif dst < 0:
            mq.append((mini - dst, mini, dst))
    pq = sorted(pq, reverse=True)
    mq = sorted(mq)
    p = 0
    for mini, dst in pq:
        if p + mini < 0:
            print('No')
            exit()
        p += dst
    for minimini, mini, dst in mq:
        if p + mini < 0:
            print('No')
            exit()
        p += dst
    if p != 0:
        print('No')
    else:
        print('Yes')

if __name__ == '__main__':
    main()