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()))
D={}
for a in A:
  if(a in D):
    D[a]+=1
  else:
    D[a]=1
    
if(max(D)-min(D)>1):
  print("No")
  exit()
  
if(len(D)==2):
  B=max(D)
  if(B-D[B-1]>0 and D[B]>=2*(B-D[B-1])):
    print("Yes")
  else:
    print("No")
  
else:
  B=max(D) # 常に同じ色の人がいる
  if(N>=2*B):
    print("Yes")
    exit()
  
  B=max(D)+1 # 全員違う色
  if(B==N):
    print("Yes")
    exit()
  print("No")
  
  
  