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>
#define N 100005
using namespace std;

int n, mx, a, c[N];
int main()
{
	int i;
	cin >> n;
	for (i = 0; i < n; i++) {
		scanf("%d", &a);
		c[a]++;
		mx = max(mx, a);
	}
	if (c[mx] + c[mx - 1] < n) {cout << "No"; return 0;}
	if (c[mx] == n) {
		if (mx == n - 1 || mx <= n / 2) cout << "Yes";
		else cout << "No";
	} else {
		if (c[mx - 1] + 1 <= mx && mx <= c[mx - 1] + c[mx] / 2) cout << "Yes";
		else cout << "No";
	}
    return 0;
}