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>

int a[100005],n,k;

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",&a[i]);
    std::sort(a+1,a+n+1);

    if(a[1]==a[n])puts(a[1]==n-1||(a[1]&&a[1]<=n/2)?"Yes":"No");
    else
    {
	for(k=1;a[k]==a[k+1];++k);
	if(a[k+1]!=a[n]||a[n]-a[k]>1)puts("No");
	else a[n]-=k,puts(a[n]>0&&a[n]<=(n-k)/2?"Yes":"No");
    }
    
    return 0;
}