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>
using namespace std;
int i,j,k,n,m,a[210001],t1,t2;
bool check(int x1,int x2,int v1,int v2){
	int i,j,k;
	if (v1==v2){
		if (v1==n-1) return 1;
		return n>=2*v1;
	}else{
		if (v2<x1+1) return 0;
		k=v2-x1;
		return x2>=2*k;
	}
}
int main(){
	scanf("%d",&n);
	for (i=1,t1=n+1,t2=0;i<=n;i++) scanf("%d",&a[i]),t1=min(t1,a[i]),t2=max(t2,a[i]);
	if (t1+1<t2){
		puts("No");return 0;
	}
	for (i=1,j=k=0;i<=n;i++){
		if (a[i]==t1) j++;
		if (a[i]==t2) k++;
	}
	puts(check(j,k,t1,t2)?"Yes":"No");
	return 0;
}