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()))
A=sorted(A)
if (A[-1]-A[0])>1:
  print('No')
  exit()
elif (A[-1]-A[0])==0:
  if 1<=A[0] and A[0]<=N//2:
    print('Yes')
    exit()
  else:
    if A[0]+1==N:
      print('Yes')
      exit()    
    else:
      print('No')
      exit()
  
import bisect
a=bisect.bisect_right(A,A[0])
#少ない数a,多い数b
b=N-a
if b==1:
  print('No')
  exit()
if (a-1)+1<=A[0] and A[0]<=(a-1)+b//2 and a+1<=A[-1] and A[-1]<=a+b//2:
  print('Yes')
else:
  print('No')