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;

int a[100010];

int main(){
	int n; scanf("%d", &n);
	int maxj = -0x3f3f3f3f, minj = 0x3f3f3f3f;
	for (int i = 0; i < n; i++){
		scanf("%d", &a[i]);
		maxj = max(maxj, a[i]);
		minj = min(minj, a[i]);
	}
	if (maxj - minj > 1){
		printf("No\n");
		return 0;
	}
	if (maxj == minj){
		if (maxj * 2 <= n || maxj + 1 == n) printf("Yes\n");
		else printf("No\n");
		return 0;
	}
	int tot = maxj, all = n;
	for (int i = 0; i < n; i++){
		if (a[i] == minj) tot--, all--;
	}
	if (tot > 0 && tot * 2 <= all) printf("Yes\n");
	else printf("No\n");
	return 0;
}
