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<bits/stdc++.h>
#define L long long
using namespace std;
int n,x[100010],l=1e9,r,a,b;
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  {
	   scanf("%d",&x[i]);
	   l=min(l,x[i]);
	   r=max(r,x[i]);
	  }
	for(i=1;i<=n;i++)
	  if(x[i]==l)
	    a++;
	  else if(x[i]==r)
	    b++;
	if(a+b<n || r>l+1)
	  {
	   printf("No\n");
	   return 0;
	  }
	if(l==r)
	  i=1,j=n/2;
	else
	  i=a+1,j=a+b/2;
	if(i<=r && r<=j || l==r && l==n-1)
	  printf("Yes\n");
	else
	  printf("No\n");
	return 0;
}
