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 kakko(S):
    cum = 0
    mi = 0
    for s in S:
        cum += 1 if s == '(' else -1
        mi = min(mi, cum)
    return (-mi, cum - mi)

N = int(input())
S = [kakko(input()) for _ in range(N)]

plus = []
minus = []

for l, r in S:
    if l <= r:
        plus.append((l, r))
    else:
        minus.append((l, r))

plus.sort(key=lambda a: a[0])
minus.sort(key=lambda a: a[1], reverse=True)
M = 0
for l, r in (plus + minus):
    M -= l
    if M < 0:
        print('No')
        exit()
    M += r

print('Yes' if M == 0 else 'No')
