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;
typedef long long ll;
const ll N=1e5+5,mod=1e9+7;
ll n,a[N],mx=0,mn=N;
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin>>n;
    for(ll i=0;i<n;i++){
        cin>>a[i];
        mx=max(mx,a[i]);
        mn=min(mn,a[i]);
    }
    if(mx>mn+1)return cout<<"No" , 0;

    if(mx==mn){
        if(mn==n-1 || mn*2<=n)cout<<"Yes";
        else cout<<"No";
    }
    else{
        ll cnt=0;for(ll i=0;i<n;i++)cnt+=(a[i]==mn);
        if(cnt<mx && 2*(mx-cnt)<=n-cnt)cout<<"Yes";
        else cout<<"No";
    }
}