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<algorithm>
using namespace std;

int main(){
	int n,a[100000],mi = 10000000,ma = -1;
	scanf("%d",&n);
	for(int i=0;i<n;i++) scanf("%d",a+i);
	for(int i=0;i<n;i++){
		mi = min(mi,a[i]);
		ma = max(ma,a[i]);
	}
	switch(ma-mi){
		case 0:{
			if(mi==n-1||(2*mi<=n&&mi>0)) printf("Yes\n");
			else printf("No\n");
			break;
		}
		case 1:{
			int x = 0;
			for(int i=0;i<n;i++) if(a[i]==mi) x++;
			if(2*(ma-x)<=n-x&&ma-x>0) printf("Yes\n");
			else printf("No\n");
			break;
		}
		default:{
			printf("No\n");
			break;
		}
	}
}
