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;
 int main(){
 	int n,a[100010],maxa=0,mina=1e9,num1=0;
 	cin>>n;
 	for(int i=1;i<=n;i++){
 		cin>>a[i];
 		if(a[i]>maxa) maxa=a[i];
 		if(a[i]<mina) mina=a[i];
	 }
	if(maxa-mina>1){
		cout<<"No";
		return 0;
	}
	for(int i=1;i<=n;i++)
	  if(a[i]==mina) num1++;
	if(maxa-mina==0){
		if(maxa==n-1||maxa*2<=n) cout<<"Yes";
		else cout<<"No";
	}
	else{
		if(num1<maxa&&n-num1>=2*(maxa-num1)) cout<<"Yes";
		else cout<<"No";
	}
	return 0;
 }