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())
S = [input() for _ in range(n)]
U = []
L = []
for s in S:
  l, r = 0, 0
  for t in s:
    if t == "(":
      r += 1
    else:
      if r > 0:
        r -= 1
      else:
        l += 1
  if l <= r:
    U.append((l, r-l))
  else:
    L.append((r, l-r))
U.sort()
L.sort()
s, t = 0, 0
for a, c in U:
  if s < a:
    print("No")
    exit()
  s += c
for a, c in L:
  if t < a:
    print("No")
    exit()
  t += c
if s != t:
  print("No")
  exit()
print("Yes")