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 itertools import chain

N = int(input())
zenhan = []
kouhan = []
for _ in range(N):
    si = input()
    last = 0
    low = last
    high = last
    for s in si:
        if s == "(":
            last += 1
        else:
            last -= 1
        low = min(low, last)
        high = max(high, last)
    if last >= 0:
        zenhan.append((-low, last, low))
    else:
        kouhan.append((low - last, last, low))
zenhan.sort()
kouhan.sort()

open_close = 0
for key, last, low in chain(zenhan, kouhan):
    if open_close + low < 0:
        ans = "No"
        break
    else:
        open_close += last
else:
    if open_close:
        ans = "No"
    else:
        ans = "Yes"
print(ans)
