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=list(map(int,input().split()))
from collections import Counter
ca=dict(Counter(a))
if len(ca.keys())>2:
  print('No')
elif len(ca.keys())==1:
  if 2*a[0]<=n or a[0]==n-1:
    print('Yes')
  else:
    print('No')
else:
  c=max(ca.keys())
  d=min(ca.keys())
  # cといった猫はその猫しかかぶっていない帽子をかぶっている
  # dといった猫はその猫以外にもかぶっている帽子をかぶっている
  if c!=d+1:
    print('No')
  else:
    tmp=c-ca[d]
    # tmp:dといった猫たちがかぶっている帽子の種類数
    if tmp>0 and 2*tmp<=ca[c]:
      print('Yes')
    else:
      print('No')
