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>
using namespace std;

const int N = 1e5 + 10;

int a[N];

int main(){
	int n, pos;
	scanf("%d",&n);
	for (int i = 1; i <= n; i++) scanf("%d",&a[i]);
	sort(a + 1, a + n + 1);
	if (a[1] + 2 <= a[n]) printf("No\n");
	else if (a[1] == a[n]){
		if (a[1] == n - 1 || n % a[1] == 0) printf("Yes\n");
		else printf("No\n");
	}
	else{
		for (int i = 1; i < n; i++){
			if (a[i] < a[i + 1]){
				pos = i;
				break;
			}
		}
		if (a[n] > pos && (n - pos) % (a[n] - pos) == 0) printf("Yes\n");
		else printf("No\n");
	}
	return 0;
}