There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
N, *A = map(int, open(0).read().split())
s = set(A)
if max(s)-min(s)>1:
  print('No')
else:
  if len(s)==1:
    if A[0]==N-1:
      print('Yes')
    elif 2*A[0]<=N:
      print('Yes')
    else:
      print('No')
  elif len(s)==2:
    N -= A.count(min(s))
    u = max(s)-A.count(min(s))
    if u<=0:
      print('No')
    elif 2*u<=N:
      print('Yes')
    else:
      print('No')
  else:
    print('No')