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<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
int main()
{
	int num;
	scanf("%d", &num);
	vector<int>v;
	for (int i = 0; i < num; i++)
	{
		int z;
		scanf("%d", &z);
		v.push_back(z);
	}
	sort(v.begin(), v.end());
	if (v[num - 1] - v[0]>1)printf("No\n");
	else if (v[0] == v[num - 1])
	{
		if (v[0] == num - 1 || v[0] <= num / 2)printf("Yes\n");
		else printf("No\n");
	}
	else
	{
		int c = 0;
		for (int i = 0; i < num; i++)if (v[i] == v[0])c++;
		if (c <= v[0] && v[0] <= c - 1 + (num - c) / 2)printf("Yes\n");
		else printf("No\n");
	}
}