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 c[100010],n;
int main(){
	int p=0,q=114514,a=0,b=0;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>c[i];
		p=max(p,c[i]);
		q=min(q,c[i]);
	}
	for(int i=0;i<n;i++){
		if(c[i]==p)a++;
		if(c[i]==q)b++;
	}
	bool ans=false;
	if(p==q){
		if(1<=p&&q<=a/2)ans=true;
		if(p==n-1)ans=true;
	}
	if(p==q+1){
		if(1+b<=p&&p<=a/2+b)ans=true;
		if(a==1)ans=false;
	}
	if(ans==true)cout<<"Yes"<<endl;
	else cout<<"No"<<endl;
	return 0;
}
