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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=100005;

int n,cnt,a,b;
int f[N];

int main(){
	int i;
	scanf("%d",&n);
	for (i=1;i<=n;i++) scanf("%d",&f[i]);
	sort(f+1,f+1+n);
	if (f[n]>f[1]+1){
		printf("No\n");
		return 0;
	}
	if (f[n]==f[1]){
		if (f[n]*2<=n||f[n]==n-1) printf("Yes\n");
		else printf("No\n");
		return 0;
	}
	for (i=1;i<=n;i++) if (f[i]==f[1]) a++;
	cnt=n-a; b=f[n]-a;
	if (b*2<=cnt&&b>0) printf("Yes\n");
	else printf("No\n");
	return 0;
}