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())
from collections import deque
L = deque([])
R = deque([])

for i in range(N):
  S = input()
  l = [0]*len(S)
  if S[0]=='(':
    l[0]=1
  else:
    l[0]=-1
  for j in range(1,len(S)):
    if S[j]=='(':
      l[j] = l[j-1] + 1
    else:
      l[j] = l[j-1] - 1
  if l[-1] < 0:
    R.append([min(l)-l[-1], -l[-1], min(l), l[-1]])
  else:
    L.append([min(0,min(l)),l[-1]])
    
R = sorted(R, key = lambda x:x[0])
L = sorted(L, key = lambda x:x[0], reverse = True)
now = 0
judge = True
    
for l in L:
  if now + l[0]<0:
    judge = False
    break
  else:
    now += l[1]
    
for r in R:
  if now+r[2]<0:
    judge = False
    break
  else:
    now += r[3]
    
if now!=0:
  judge = False
  
if judge:
  print('Yes')
else:
  print('No')
    