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>
#include<queue>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
using namespace std;
const int N=100005;
int a[N];
int main()
{
	int n;scanf("%d",&n);
	rep(i,1,n)scanf("%d",&a[i]);int ma=0;
	rep(i,1,n)ma=max(ma,a[i]);rep(i,1,n)if(a[i]!=ma && a[i]!=ma-1){puts("No");return 0;}
	int cnt=0;rep(i,1,n)if(a[i]==ma-1) cnt++;
	if(!cnt){
		if(a[1]!=n-1 && a[1]>n/2){puts("No");return 0;}
		puts("Yes");return 0;
	}
	if(cnt>=ma||2*(ma-cnt)+cnt>n){puts("No");return 0;}
	puts("Yes");
	return 0;
}