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;
const int maxn=100010;
int n,a[maxn];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	if(a[n]-a[1]>1)printf("No");
	else if(a[n]==a[1])printf(n==a[1]+1||n>=(a[1]<<1)?"Yes":"No");
	else{
		int p=0,q=0;
		for(int i=1;i<=n;i++)(a[i]==a[1]?p:q)++;
		if(a[1]<p)printf("No");
		else printf(n-p>=((a[1]-p+1)<<1)?"Yes":"No");
	}
	return 0;
}