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 maxn=100005;

int n,a[maxn],mx,cnt;
bool fail;

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	sort(a+1,a+n+1),mx=a[n]; 
	if(a[n]-a[1]>1)return puts("No"),0;
	if(a[1]==a[n])if(mx==n-1||2*mx<=n)return puts("Yes"),0;
	if(a[n]!=a[1])
	{
		for(cnt=1;a[cnt]==a[1];cnt++);cnt--;
		if(cnt>a[1])return puts("No"),0;
		mx-=cnt,n-=cnt;
		if(mx*2<=n)return puts("Yes"),0;
	}
	return puts("No"),0;
}