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
import sys
N = int(input())
B1 = []
B2 = []

def change(S):
    MIN = 0
    SUM = 0
    for i in S:
        if i == ')':
            SUM -= 1
            MIN = min(MIN, SUM)
        else:
            SUM += 1
    MIN *= -1
    return (MIN, SUM)

for _ in range(N):
    b = change(input())
    if b[1] > 0:
        B1.append(b)
    else:
        B2.append((b[0] + b[1], b[0], b[1]))

B1.sort()
B2.sort(reverse = True)

cnt = 0
for b in B1:
    if cnt < b[0]:
        print('No')
        sys.exit()
    cnt += b[1]

for b in B2:
    if cnt < b[1]:
        print('No')
        sys.exit()
    cnt += b[2]

if cnt == 0:
    print('Yes')
else:
    print('No')