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 check(li):
    b = 0
    for eb, eh in li:
        if b + eb < 0:
            return False

        b += eh

    return True


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

l = []
r = []
sm = 0
for word in s:
    h = 0
    b = 0
    for e in word:
        if e == "(":
            h += 1
        else:
            h -= 1

        b = min(b, h)

    if h > 0:
        l.append([b, h])
    else:
        r.append([b-h, -h])

    sm += h

l.sort(reverse=True)
r.sort(reverse=True)

if check(l) and check(r) and sm == 0:
    ans = "Yes"
else:
    ans = "No"
print(ans)
