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 <cmath>
#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

int n,x,y,color,ans;
int a[100010];

int main(){
	scanf("%d",&n);
	color=0;
	for (int i=1;i<=n;++i){
		scanf("%d",&a[i]);
		color=max(color,a[i]);
	}
	for (int i=1;i<=n;++i){
		if (color-1>a[i]){
			puts("No");
			return 0;
		}
		if (color-1==a[i]) ++x;
	}
	y=n-x;
	if (x==0 && color==n-1){
		puts("Yes");
		return 0;
	}
	if (color==x){
		puts("No");
		return 0;
	}
	if (y/(color-x)>1) puts("Yes");
	else puts("No");
}