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())
ls, rs = [], []

def check(sl):
    h = 0
    for t in sl:
        b = h + t[0]
        if b < 0:
            return False
        h += t[1]
    return True

total = 0
for i in range(n):
    b, h = 0, 0
    S = input()
    for s in S:
        if s == '(':
            h += 1
        else:
            h -= 1
        b = min(b, h)
    if h > 0:
        ls.append((b, h))
    else:
        rs.append((b - h, -h))
    total += h
ls.sort(key=lambda x: x[0], reverse=True)
rs.sort(key=lambda x: x[0], reverse=True)
print('Yes' if check(ls) and check(rs) and total == 0 else 'No')