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
n=int(input())
a=[]
b=[]
for i in range(n):
  s=input()
  overall=0
  minimum=0
  current=0
  for j in range(len(s)):
    if s[j]=='(':
      current+=1
    else:
      current-=1
    minimum=min(current,minimum)
  overall=current
  if overall>=0:
    a.append([overall,minimum])
  else:
    b.append([overall,minimum])
finalsum=0
a=sorted(a, key=lambda t:t[1])
a.reverse()
b=sorted(b, key=lambda t:t[0]-t[1])
b.reverse()
for i in a:
  if finalsum+i[1]<0:
    print('No')
    sys.exit()
  finalsum+=i[0]
for i in b:
  if finalsum+i[1]<0:
    print('No')
    sys.exit()
  finalsum+=i[0]
if finalsum==0:
  print('Yes')
else:
  print('No')