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())
arr=list(map(int,input().split()))
amax=max(arr)
amin=min(arr)
if amax-amin>=2:
  print('No')
elif amax-amin==0:
  flag=False
  for i in range(n):
    if arr[i]!=n-1:
      break
  else:
    flag=True
  for i in range(n):
    if 2*arr[i]>n:
      break
  else:
    flag=True
  if flag==True:
    print('Yes')
  else:
    print('No')
elif amax-amin==1:
  cnt1=0
  cnt2=0
  for i in range(n):
    if arr[i]==amax-1:
      cnt1+=1
    else:
      cnt2+=1
  if cnt1<amax and 2*(amax-cnt1)<=cnt2:
    print('Yes')
  else:
    print('No')