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())
S=[input() for i in range(N)]
a,b=0,0
X=[]
Y=[]
for i in range(N):
  a,b=0,0
  for j in range(len(S[i])):
    if S[i][j]=='(':
      a+=1
    else:
      a-=1
    b=min(b,a)
  b=-b
  a=a+b
  if a>b:
    X.append((b,a))
  else:
    Y.append((b,a))
P=0
Q=0
X.sort()
for i in range(len(X)):
  P=max(P,Q+X[i][0])
  Q=Q+X[i][0]-X[i][1]
Y.sort(key=lambda x:-x[1])
for i in range(len(Y)):
  P=max(P,Q+Y[i][0])
  Q=Q+Y[i][0]-Y[i][1]
if P or Q:
  print('No')
else:
  print('Yes')