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 rep(i,n) for ((i)=1;(i)<=(n);(i)++)
#define per(i,n) for ((i)=n;(i)>=(1);(i)--)
using namespace std;
int n,i,j,a[100005],cnt[100005];
int main()
{
	cin>>n;int mx=0,mi=n+1;
	rep(i,n){cin>>a[i];mx=max(mx,a[i]);mi=min(mi,a[i]);cnt[a[i]]++;}
	if(mx-mi>1){puts("No");return 0;}
	if(mx==mi)
	{
		if(mi==n-1||mi*2<=n)
		{
			puts("Yes");
		}
		else
		{
			puts("No");
		}
	}
	else
	{
		if(cnt[mi]>mi)
		{
			puts("No");
		}
		else if(n-cnt[mi]<2*(mx-cnt[mi]))
		{
			puts("No");
		}
		else puts("Yes");
	}
	return 0;
}