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
N = int(input())

memo1 = []
memo2 = []
for i in range(N):
  S = input()
  sum_n = min_n = 0
  for s in S:
    if s == ')':
      sum_n -= 1
      min_n = min(min_n, sum_n)
    else:
      sum_n += 1
  if sum_n >= 0:
    memo1.append([min_n, sum_n])
  else:
    memo2.append([min_n-sum_n, -sum_n])

memo1.sort(reverse=True)
left = 0
for min_n, sum_n in memo1:
  if left + min_n < 0:
    print('No')
    quit()
  else:
    left += sum_n

memo2.sort(reverse=True)
right = 0
for min_n, sum_n in memo2:
  if right + min_n < 0:
    print('No')
    quit()
  else:
    right += sum_n

if left == right:
  print('Yes')
else:
  print('No')