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>
#define gg {puts("No");exit(0);}
using namespace std;
int n,a[100010],vis[100010],mn=1e9,mx=-1;
int check()
{
	if(mx>mn)
	{
		for(int i=1;i<=n;i++)vis[a[i]]++;
		n-=vis[mn],mx-=vis[mn];
		if(mx<=0)return 0;
		if(n<mx*2)return 0;
		return 1;
	}
	else if(mx==mn)
	{
		if(n==mn+1)return 1;
		if(n>=mx*2)return 1;
		return 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)gg;
	if(check())puts("Yes");
	else puts("No");
} 