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;
int a[100005];

int main() {
	
	cin>>N; 
	
	int Mx=0,Mn=1234567;
	
	for(int i=0; i<N; i++){
		cin>>a[i];
		Mx=max(Mx,a[i]);
		Mn=min(Mn,a[i]);
		
	}
	
	if(Mx-Mn>=2){
		cout<<"No"<<endl;
	}
	
	if(Mx-Mn==0){
		if(a[0]==N-1||2*a[0]<=N) cout<<"Yes"<<endl;
		else cout<<"No"<<endl;
	}
	
	if(Mx-Mn==1){
		
		int cnt=0;
		
		for(int i=0; i<N; i++){
			if(a[i]==Mn) cnt++;
		}
		
		if(2*Mx-cnt<=N&&Mx-cnt>=1) cout<<"Yes"<<endl;
		else cout<<"No"<<endl;
	}
	
	
	return 0;
}