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>
#include<cstring>
#include<algorithm>
#define N 100010
using namespace std;
int n, sum[N], x, s;
int main(){
	scanf("%d", &n);
	memset(sum, 0, sizeof(sum));
	for(int i=1; i<=n; i++){scanf("%d", &x); sum[x]++;}
	s=0; for(int i=1; i<=n-1; i++)if(sum[i]){x=i; s++;}
	if(s>=3){printf("No"); return 0;}
	if(s==1){
		if(x==n-1||x<=n/2)printf("Yes"); else printf("No");
		return 0;
	}
	if(!sum[x-1]){printf("No"); return 0;}
	if(sum[x-1]>=x){printf("No"); return 0;}
	if(x-sum[x-1]<=(n-sum[x-1])/2)printf("Yes"); else printf("No");
	return 0;
}