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())
plus_bracket = []
minus_bracket = []

for _ in range(n):
  mini = 0
  cur = 0
  for bracket in input():
    if bracket == '(':
      cur += 1
    else:
      cur -= 1
    if cur < mini:
      mini = cur
  if cur > 0:
    plus_bracket.append([-mini, cur])
  else:
    minus_bracket.append([cur - mini, -cur])

success = True
cur = 0
plus_bracket.sort()
minus_bracket.sort()
for bracket in plus_bracket:
  if cur < bracket[0]:
    success = False
    break
  cur += bracket[1]
back_cur = 0
for bracket in minus_bracket:
  if back_cur < bracket[0]:
    success = False
    break
  back_cur += bracket[1]
if cur != back_cur:
  success = False

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