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 a[100005];
int main()
{
	bool flag=1;
	int t,mx,mn;
	scanf("%d",&t);
	scanf("%d",a+1);
	mx=mn=a[1];
	for(int i=2;i<=t;++i)
	{
		scanf("%d",a+i);
		if(a[i]!=a[i-1]) flag=0;
		mx=max(mx,a[i]);mn=min(mn,a[i]);
	}
	if(mx>mn+1) {puts("No");return 0;}
	int n=0,m=0;
	for(int i=1;i<=t;++i)
	if(a[i]==mx) ++n;
	else ++m;
	if(!flag)
	{
		if(mx-m<=0) {puts("No");return 0;}
		if(2*(mx-m)<=n) puts("Yes");
		else puts("No");
	}
	else
	{
		if(mx==t-1) {puts("Yes");return 0;}
		if(mx<=t/2) puts("Yes");
		else puts("No");
	}
}