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())

#INF = float('inf')

def check(A):
  th = 0 #高さの合計
  for i in range(len(A)):
    b = A[i][0]
    h = A[i][1]
    if th + b < 0:
      return False
    else:
      th += h
  return True
    

L = []
R = []
goukei = 0
for i in range(N):
  temp = str(input())
  b= 0 #最下点
  h = 0 #ゴールの位置
  for j in range(len(temp)):
    if temp[j] == "(":
      h += 1
    else:
      h -= 1
    b = min(b,h)
  if h > 0:
    L.append([b,h])
  else:
    R.append([b-h,-h])
  goukei += h

L.sort(reverse=True)
R.sort(reverse=True)
#print(L,R)

if check(L) and check(R) and goukei == 0:
  print("Yes")
else:
  print("No")