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 a[100007];
int main(){
	int n;
	int m[2]={100007,0};
	bool s=false;
	int i,j,k;
	cin>>n;
	for(i=0;i<n;i++){
		cin>>a[i];
		if(a[i]<m[0])m[0]=a[i];
		if(m[1]<a[i])m[1]=a[i];
	}
	if(m[0]==m[1]){
		if(n>=a[0]*2 || n==a[0]+1)s=true;
	}
	if(m[1]-m[0]==1){
		for(i=0,k=0;i<n;i++){
			if(a[i]==m[0])k++;
		}
		if(n-k>1){
			j=k+(n-k)/2;
			if(k+1<=m[1] && m[1]<=j)s=true;
		}
	}
	if(s)cout<<"Yes"<<endl;
	else cout<<"No"<<endl;
	return 0;
}
	
