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())
L=sorted(list(map(int,input().split())))
if L[-1]-L[0]>1:
  s='No'
elif L[-1]-L[0]==1:
  c=L.count(L[0])
  s = ('Yes'if c<L[-1] and 2*(L[-1]-c)<=n-c else 'No')
else:
  s = ('Yes'if L[0]==n-1 or 2*L[-1]<=n else 'No')
print(s)