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>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int maxn = 100010;
int a[maxn];

int main()
{
	int n;
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	bool flg = false;
	if (a[n] - a[1] > 1) {}
	else if (a[1] == a[n])
	{
		if (a[1] == n-1) flg = true;
		else if (a[1]*2<=n) flg = true;
	}
	else
	{
		int p = upper_bound(a+1,a+n+1,a[1]) - a;
		int x = p-1, y = n-x;
		if (a[n] >= x+1 && a[n] <= x+y/2) flg = true;
	}
	puts(flg ? "Yes" : "No");
	return 0;
}
