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
from operator import itemgetter
from itertools import chain


N = int(input())
L = []
R = []
for i in range(N):
    S = input()
    low = 0
    var = 0

    for s in S:
        if s == '(':
            var += 1
        else:
            var -= 1
        low = min(low, var)
    
    if var >= 0:
        L.append((low, var))
    else:
        R.append((low, var))

L.sort(key=itemgetter(0), reverse=True)
R.sort(key=lambda x: x[0] - x[1])
pos = 0
for i, (low, var) in enumerate(chain(L, R)):
    if pos + low < 0:
        ans = 'No'
        break
    pos += var
else:
    ans = 'Yes' if pos == 0 else 'No'
print(ans)
