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>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<ctime>
#define N 100010
using namespace std;
int n,a[N];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	int mx=0,mn=n;
	for(int i=1;i<=n;i++)mx=max(mx,a[i]),mn=min(mn,a[i]);
	bool flag=1;
	for(int i=1;i<=n;i++)if(a[i]!=n-1)flag=0;
	if(flag){cout<<"Yes";return 0;}
	int cnt=0;
	if(mx-mn>1){cout<<"No";return 0;}
	for(int i=1;i<=n;i++)
	if(a[i]<mx)++cnt;
	if(mx<cnt||2*(mx-cnt)>n-cnt||(n>cnt&&(mx-cnt<1)))cout<<"No";
	else cout<<"Yes";
	return 0;
}