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 = []
for i in range(n):
  s.append(input())

ls = []
rs = []
tot = 0
for si in s:
  b = 0
  h = 0
  for c in si:
    if c == '(':
      h += 1
    else:
      h -= 1
    b = min(h,b)
  if h > 0:
    ls.append((b,h))
  else:
    rs.append((b-h,-h))
  tot += h
ls.sort(reverse = True)
rs.sort(reverse = True)

def check(x):
  t = 0
  for bx,hx in x:
    if t+bx < 0:
      return False
    t += hx
  return True

if check(ls) and check(rs) and tot == 0:
  print('Yes')
else:
  print('No')
