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>
const int INF=1e9,MOD=1e9+7;
const long long LINF=1e18;
using namespace std;
#define int long long
//template

//main
signed main(){
  int N;cin>>N;
  std::vector<int> v(N);
  for(int i=0;i<N;i++)cin>>v[i];
  int mi=LINF,ma=0;
  for(int i=0;i<N;i++)mi=min(mi,v[i]);
  for(int i=0;i<N;i++)ma=max(ma,v[i]);
  if(ma-mi>1){cout<<"No"<<endl;return 0;}
  if(ma==mi){
    if(ma<=N/2||ma==N-1)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
  }
  int c=0;
  for(int i=0;i<N;i++)c+=ma-v[i];
  if(0<(ma-c)*2&&(ma-c)*2<=N-c)cout<<"Yes"<<endl;
  else cout<<"No"<<endl;
}
