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<cstdlib>
#include<algorithm>
#define MAXN 100005

int n;
int a[MAXN];
int ma,mi=(int)1e9;
int cnt;
int p;

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",a+i);
		ma=std::max(ma,a[i]);
		mi=std::min(mi,a[i]);
	}
	if(ma-mi>1||ma>n-1){
		p=0;
	}else if(ma==mi){
		if(ma==n-1) p=1;
		else if(ma*2<=n) p=1;
		else p=0; 
	}else{
		for(int i=1;i<=n;i++)
			if(a[i]==mi) cnt++;
		if(2*(ma-cnt)<=n-cnt&&ma>cnt) p=1;
		else p=0;
	}
	printf("%s\n",p?"Yes":"No");
}




