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
input = sys.stdin.readline

def main():
  n = int(input())
  
  a = []
  b = []
  for i in range(n):
    s = input()
    c1, c2 = 0, 0
    for i in range(len(s)):
      if s[i] == "(":
        c2 += 1
      if s[i] == ")":
        if c2:
          c2 -= 1
        else:
          c1 += 1
    if c1 >= c2:
      b.append((c2, c1))
    else:
      a.append((c1, c2))
  a.sort()
  b.sort(reverse=True)
  ans = False
  sub = 0
  for value in a:
    k1, k2 = value[0], value[1]
    if sub < k1:
      ans = True
      break
    sub += k2-k1
  for value in b:
    k2, k1 = value[0], value[1]
    if ans or sub < k1:
      ans = True
      break
    sub += k2-k1
  print("No" if ans or sub else "Yes")

if __name__ == "__main__":
  main()