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;
const int N=1e5+50;
int n,a[N],mn=1e5,mx,nn;
void fail(){puts("No");exit(0);}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]),mn=min(mn,a[i]),mx=max(mx,a[i]);
	if(mx-mn>1)fail();
	if(mx>mn){
		for(int i=1;i<=n;i++)if(a[i]==mn)nn++;
		if(nn+1>mx||nn==n-1)fail();
		nn+=(n-nn)/2;if(nn<mx)fail();
		puts("Yes");
	}
	else{
		if(mx!=n-1&&n/2<mx)fail();
		puts("Yes");
	}
	return 0;
}