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 n,i,k,x,sx,y,sy;
int read(){
	char c=getchar();int k=0;for (;c<48||c>57;c=getchar());
	for (;c>47&&c<58;c=getchar()) k=(k<<3)+(k<<1)+c-48;return k;
}
int main(){
	for (n=read(),x=n,i=1;i<=n;i++){
		k=read();
		if (k<x) x=k,sx=0;if (k==x) sx++;
		if (k>y) y=k,sy=0;if (k==y) sy++;
	}
	if (y-x>1){puts("No");return 0;}
	if (x==y){
		puts(x==n-1||x<=n/2?"Yes":"No");
		return 0;
	}
	y-=sx;puts(y>=1&&y<=sy/2?"Yes":"No");
}