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<algorithm>
#define MN 111100
using namespace std;

int n,s,S,a[MN],ma=0,mi=1e9;
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),ma=max(ma,a[i]),mi=min(mi,a[i]);
	
	if (ma-mi>1) return puts("No"),0;
	if (ma==mi) return puts(n>=ma*2||n==ma+1?"Yes":"No"),0;
	s=ma;S=n;
	for (int i=1;i<=n;i++) if (a[i]==mi) s--,S--;
	puts(S>=s*2&&s>0?"Yes":"No");
}