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()))
from collections import Counter
c=sorted(Counter(A).most_common(),reverse=True)
r=0
if len(c)==2 and c[0][0]==c[1][0]+1 and 0<c[0][0]-c[1][1]<=c[0][1]//2:
    r=1
elif len(c)==1 and (c[0][0]==c[0][1]-1 or c[0][0]<=c[0][1]//2):
    r=1
print(['No','Yes'][r])