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.sort()
if a[n-1]-a[0]>=2:
  print('No')
  exit()
if a[n-1]==a[0]:
  if a[0]==n-1 or 2*a[0]<=n:
    print('Yes')
  else:
    print('No')
else:
  x=a[0]
  cnt=0
  for i in range(n):
    if a[i]==x:
      cnt+=1
    else:
      break
  if cnt<a[n-1] and 2*(a[n-1]-cnt)<=n-cnt:
    print('Yes')
  else:
    print('No')