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())
arr1=[]
arr2=[]
for _ in range(n):
  s=input()
  cnt1=0
  cnt2=0
  for i in range(len(s)):
    if s[i]=='(':
      cnt1+=1
    else:
      if cnt1==0:
        cnt2+=1
      else:
        cnt1-=1
  if cnt1-cnt2>=0:
    arr1.append([cnt1,cnt2])
  else:
    arr2.append([cnt1,cnt2])
arr1=sorted(arr1,key=lambda x:x[1])
arr2=sorted(arr2,reverse=True,key=lambda x:x[0])
arr=arr1+arr2
cnt=0
for a,b in arr:
  if b>cnt:
    print('No')
    break
  else:
    cnt+=a-b
else:
  if cnt==0:
    print('Yes')
  else:
    print('No')