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>
using namespace std;
int a[100000+10],n;
int cnt;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i) scanf("%d",&a[i]);
	sort(a+1,a+1+n);
	if (a[n]-a[1]>1) return printf("No"),0;
	if (a[1]==a[n]) return printf("%s",n==a[1]+1||n>=a[1]*2?"Yes":"No"),0;
	//if (a[1]    )
	for(int i=1;i<=n;++i) if (a[i]==a[1]) ++cnt;
	if (cnt>a[1]) return printf("No"),0;
	return printf("%s",(n-cnt)>=(a[n]-cnt)*2?"Yes":"No"),0;
	//return printf("%s",a[1]==a[2]?:)
}