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())
As = []
Bs = []

for _ in range(N):
  c = 0
  m = 0
  for s in input():
    if s == '(':
      c += 1
    elif s == ')':
      c -= 1
    m = min(m, c)
  if c >= 0:
    As.append((-m, c - m))
  else:
    Bs.append((-m, c - m))

As.sort(key=lambda x: x[0])
Bs.sort(key=lambda x: x[1], reverse=True)

f = True
c = 0
for (l, r) in As:
  if c < l:
    f = False
    break
  c += r - l
if f:
  for (l, r) in Bs:
    if c < l:
      f = False
      break
    c += r - l

f = f and (c == 0)

if f:
  print('Yes')
else:
  print('No')