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
#include<cstdio>
int main(){
	int N;scanf("%d",&N);
	int mx=0,mxc,mn=N,mnc;
	for(int i=0,a;i<N;i++){
		scanf("%d",&a);
		a>mx?mx=a,mxc=1:a==mx?mxc++:1;
		a<mn?mn=a,mnc=1:a==mn?mnc++:1;
	}
	puts(mx==mn&&(mx==N-1||mx<=N/2)||mx==mn+1&&mx-mnc>0&&mx-mnc<=mxc/2?"Yes":"No");
}