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 <algorithm>
#include <vector>
#include <string>
#define int long long
using namespace std;
signed main() {
	int n; cin >> n;
	int a[123456];
	int m = 0, M = 0;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		if (!i) {
			m = a[i]; M = a[i];
		}
		else {
			m = min(m, a[i]);
			M = max(M, a[i]);
		}
	}
	if (M - m > 1) {
		cout << "No\n";
		return 0;
	}
	else if (m == M)cout << (M == n - 1 || M * 2 <= n ? "Yes\n" : "No\n");
	else {
		int s = 0;
		for (int i = 0; i < n; i++)if (a[i] == m)s++;
		cout << ((s <= m && M <= s + (n - s) / 2) ? "Yes\n" : "No\n");
	}
	return 0;
}