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(x) for x in input().split()]
ma=max(A)
mi=min(A)
ans=True

if ma-mi > 1:
  ans=False
elif ma==mi:
  if ma!=N-1 and ma*2 > N:
    ans=False
else:
  uniq=ma*N - sum(A)
  no_uni=N-uniq
  if no_uni==1:
    ans=False
  else:
    if uniq >= ma or 2*(ma-uniq) > no_uni:
      ans=False
if ans:
  print("Yes")
else:
  print("No")