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<cstring>
#include<algorithm>
using namespace std;

const int N=100005;

int n,a[N];

int main()
{
	scanf("%d",&n);int mx=0;
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),mx=max(mx,a[i]);
	int s=0;
	for (int i=1;i<=n;i++)
	{
		if (a[i]<mx-1||a[i]>mx) {puts("No");return 0;}
		if (a[i]!=mx) s++;
	}
	if (!s&&mx==n-1) puts("Yes");
	else if (mx<=s||mx>s&&(mx-s)*2>n-s) puts("No");
	else puts("Yes");
	return 0;
	return 0;
}