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=int(input())
a=[int(i) for i in input().split()]

if len(set(a))>=3:
  print('No')
elif len(set(a))==1:
  if a[0]==n-1 or 1 <= a[0] <=n//2:
    print('Yes')
  else:
    print('No')
else:
  m=max(a)
  s=min(a)
  c=sum([1 for i in a if i==m])
  if n-m+1<=c<=n-(m-(n-m)) and s==m-1:
    print('Yes')
  else:
    print('No')