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())
s=[list(input()) for i in range(n)]
L1=[]
L2=[]
for i in range(n):
  ct3=0
  l=[0]
  for j in s[i]:
    if j=='(':
      ct3+=1
      l.append(ct3)
    else:
      ct3-=1
      l.append(ct3)
  if l[-1]>=0:
    L1.append((min(l),l[-1]))
  else:
    L2.append((min(l)-l[-1],-l[-1]))

L1.sort()
L1.reverse()
ct4=0
for i in L1:
  if ct4+i[0]<0:
    print('No')
    sys.exit()
  ct4+=i[1]

L2.sort()
L2.reverse()
ct5=0
for i in L2:
  if ct5+i[0]<0:
    print('No')
    sys.exit()
  ct5+=i[1]

if ct4!=ct5:
  print('No')
  sys.exit()

print('Yes')