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 f():
    N = int(input())
    UP = []
    DOWN = []

    for _ in range(N):
        S = input()
        c = 0
        minC = 0

        for s in S:
            if s == '(':
                c += 1
            else:
                c -= 1
                minC = min(minC, c)

        if c >= 0:
            UP.append((minC, c))
        else:
            DOWN.append((c - minC, c))


    c = 0
    for up in sorted(UP, reverse=True):
        if c + up[0] < 0:
            return False

        c += up[1]

    for down in sorted(DOWN, reverse=True):
        if c + down[1] - down[0] < 0:
            return False

        c += down[1]

    if c != 0:
        return False

    return True


if  f():
    print('Yes')
else:
    print('No')
