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;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int main(){
  int N; cin>>N;
  vector<int> v(N);
  rep(i,N) cin>>v[i];
  sort(v.begin(),v.end());
  if(v[0]==v[N-1]){
    if(v[0]==N-1||v[0]<=N/2) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
  }else if(v[N-1]-v[0]==1){
    int cnt=1;
    for(int i=1;i<N;i++){
      if(v[i]==v[i-1]) cnt++;
      else break;
    }
    if(v[N-1]<=cnt+(N-cnt)/2&&v[N-1]>cnt) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
  }else{
    cout<<"No"<<endl;
  }
  return 0;
}
