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())
lst_left = []
lst_right = []
total = 0
for i in range(n):
  s = input()
  h = 0
  b = 0
  for e in s:
    if e == "(":
      h += 1
    else:
      h -= 1
      b = min(b, h)
  if h>=0:
    lst_left.append((b, h))
  else:
    lst_right.append((b-h, -h))
  total += h
#lst_left = sorted(lst_left, key=lambda x:x[1], reverse=True)
lst_left = sorted(lst_left, key=lambda x:x[0], reverse=True)
#lst_right = sorted(lst_right, key=lambda x:x[1], reverse=True)
lst_right = sorted(lst_right, key=lambda x:x[0], reverse=True)

if total != 0:
  print("No")
  exit()
h = 0
for i in range(len(lst_left)):
  if h + lst_left[i][0] < 0:
    print("No")
    exit()
  else:
    h += lst_left[i][1]
h = 0
for i in range(len(lst_right)):
  if h + lst_right[i][0] < 0:
    print("No")
    exit()
  else:
    h += lst_right[i][1]
print("Yes")
  
