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>

using namespace std;
int n,x,mn,un,i,mx,num;
int main()
{
    cin>>n;mn=n+1;
    for(i=1;i<=n;i++)
    {
        cin>>x;
        if(x<mn) mn=x,un=0;
        if(x>mx) mx=x,num=0;
        if(x==mn) un++;
        if(x==mx) num++;
    }
    if((mx==mn&&(2*mx<=n||mx==n-1))||(mx!=mn&&un<mx&&mx-mn==1&&num/2+un-1>=mn)) cout<<"Yes";
    else cout<<"No";
    return 0;
}
