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())
dif = [0] * N
mini = [0] * N
for _ in range(N):
    S = input()
    m = 0
    now = 0
    for i in range(len(S)):
        if S[i] == '(':
            now += 1
        else:
            now -= 1
        m = min(m, now)
    dif[_] = now
    mini[_] = m

sum = 0
for i in range(N):
    sum += dif[i]
if sum != 0:
    print('No')
    sys.exit()

plus = []
minus = []
for i in range(N):
    if dif[i] >= 0:
        plus.append((mini[i], dif[i]))
    else:
        minus.append((dif[i] - mini[i], mini[i], dif[i]))
plus.sort(reverse=True)
minus.sort(reverse=True)


now = 0
for i in range(len(plus)):
    if now + plus[i][0] < 0:
        print('No')
        sys.exit()
    now += plus[i][1]

for i in range(len(minus)):
    if now + minus[i][1] < 0:
        print('No')
        sys.exit()
    now += minus[i][2]
print('Yes')
