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
def f(s):
  m=0
  n=0
  for i in s:
    if i==")":n-=1
    else:n+=1
    m=min(m,n)
  return [m,n]
n=int(input())
s=[input()for _ in range(n)]
mab=[]
pab=[]
for i in range(n):
  ab=f(s[i])
  if sum(ab)>0:pab.append(ab)
  else:mab.append(ab)
pab.sort(reverse=1)
mab.sort(key=lambda x:x[0]-x[1])
#print(pab)
#print(mab)
ab=pab+mab
n=0
for a,b in ab:
  if n+a<0:exit(print("No"))
  n+=b
  if n<0:exit(print("No"))
if n==0:print('Yes')
else:print('No')