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>
using namespace std;
int a[100005];
int main(int argc, char** argv) {
	int n,mn=1e9,mx=0,cnt=0;
	cin >> n;
	for(int i=1;i<=n;i++)
	{
		cin >> a[i];
		if(a[i]==mn)
			++cnt;
		if(a[i]<mn)
		{
			mn=a[i];
			cnt=1;
		}
		if(a[i]>mx)
			mx=a[i];
	}
	if(mx==mn)
	{
		if(a[1]==n-1)
			puts("Yes");
		else if(a[1]<=n/2)
			puts("Yes");
		else puts("No");
		return 0;
	}
	if(mx-mn>=2)
		puts("No");
	else if((n-cnt)/2+cnt<mx||cnt+1>mx)
		puts("No");
	else puts("Yes");
	return 0;
}
//dlstxdy!