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>
using namespace std;
int n,num,maxn,ans=1,minn,a[100001];
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)cin>>a[i];
    sort(a+1,a+1+n);
    minn=a[1],maxn=a[n];
    if(minn<maxn-1||maxn>=n)ans=0;
    if(maxn==minn)
    {
        if(minn+1!=n&&minn*2>n)ans=0;
    }
    else
    {
        for(int i=1;i<=n;i++)if(a[i]==minn)num++;
        n-=num;maxn-=num;
        if(minn<num)ans=0;
        else if(maxn*2>n)ans=0;    
    }
    if(ans)cout<<"Yes";
	else cout<<"No";
    return 0;
}