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,inc,dec=int(input()),[],[]
for _ in range(n):
  s,d,r=input(),0,0
  for c in s:
    d=d+(1 if c=='(' else -1)
    r=max(r,-d)
  (dec if d<0 else inc).append((d,r))
inc.sort(key=lambda x:x[1])
dec.sort(key=lambda x:x[0]+x[1])
p1,p2,ok=0,0,True
for s in inc:
  ok&=s[1]<=p1
  p1+=s[0]
for s in dec:
  ok&=p2>=s[0]+s[1]
  p2-=s[0]
ok&=p1==p2
print('Yes'if ok else'No')
    
