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())
L = []
R = [] # Rは右から見た値を入れる
for _ in range(n):
  s = input()
  btm = 0
  total = 0
  for c in s:
    if c == "(":
      total += 1
    else:
      total -= 1
    btm = min(btm, total)
  if total > 0:
    L.append((btm, total))
  else:
    R.append((btm - total, - total))
    
L.sort(key=lambda x: (-x[0], -x[1]))
R.sort(key=lambda x: (-x[0], -x[1]))

Lcrr_end = 0
for b, e in L:
  if Lcrr_end + b < 0:
    print("No")
    exit()
  Lcrr_end += e

Rcrr_end = 0
for b, e in R:
  if Rcrr_end + b < 0:
    print("No")
    exit()
  Rcrr_end += e

if Lcrr_end - Rcrr_end == 0:
  print("Yes")
else:
  print("No")