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())

tleft = 0
tright = 0
a = []
b=  []
for _ in range(N):
  s = input()
  left = 0
  lmin = 0
  for c in s:
    if c == "(":
      left += 1
    else: # ")"
      left -= 1
      lmin = min(lmin,left)
  #
  if left >= 0:
    if lmin == 0:
      tleft += left
    else:
      a.append([left,lmin])
  else:
    if left <= lmin:
      tright += left
    else:
      b.append([left,lmin])
#
a.sort(key=lambda x:-x[1])
b.sort(key=lambda x:x[1])

for left, lmin in a:
  if tleft + lmin < 0:
    print("No")
    exit(0)
  else:
    tleft += left
#
for left, lmin in b:
  if tleft + lmin < 0:
    print("No")
    exit(0)
  else:
    tleft += left
#
if tleft + tright == 0:
  print("Yes")
else:
  print("No")
#
