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
n = int(input())


def _kakko(s):
    l, lr = 0, 0
    for c in s:
        if c == ')':
            if lr == 0:
                l = l + 1
            else:
                lr = lr - 1
        else:
            lr = lr + 1
    return (l, lr)


s = [_kakko(input()) for _ in range(n)]

sl = [ss for ss in s if ss[1] >= ss[0]]
sr = [ss for ss in s if ss[1] < ss[0]]

sl.sort(key=lambda x: x[0])
sr.sort(key=lambda x: x[1], reverse=True)

r = 0
for ss in sl:
    if ss[0] > r:
        print('No')
        exit(0)
    r = r + ss[1] - ss[0]

for ss in sr:
    if ss[0] > r:
        print('No')
        exit(0)
    r = r + ss[1] - ss[0]

if r != 0:
    print('No')
    exit(0)

print('Yes')
