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
def answer(x):
  print(x)
  exit()

N=int(input())
A=list(map(int,input().split()))
if len(set(A))>=3:
  answer('No')
if len(set(A))==1:
  if N//2>=A[0] or A[0]==N-1:
    answer('Yes')
  else:
    answer('No')
A.sort()
if A[0]+1<A[-1]:
  answer('No')
X=1
for i in range(N-1):
  if A[i]==A[i+1]:
    X+=1
  else:
    break
if X==N-1:
  answer('No')
if X+1<=A[-1]<=X+(N-X)//2:
  answer('Yes')
else:
  answer('No')
