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

using namespace std;

int a[100010];

int main()
{
	//freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	int n;scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	int mi=a[1],ma=a[1];
	for (int i=2;i<=n;i++)
	{
		mi=min(mi,a[i]);ma=max(ma,a[i]);
	}
	if (mi+1<ma) {puts("No");return 0;}
	if (mi==ma)
	{
		if (mi<=n/2||mi==n-1) puts("Yes"); else puts("No");
		return 0;
	}
	int s=0;
	for (int i=1;i<=n;i++) if (a[i]==mi) s++;
	if (s+1<=ma&&ma<=s+(n-s)/2) puts("Yes"); else puts("No");
	return 0;
}
