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 main() {
	int N, a[100000];
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> a[i];
	}
	sort(a, a + N);
	if (a[0] == a[N - 1]) {
		if (a[0] == N - 1 || a[0] * 2 <= N) cout << "Yes";
		else cout << "No";
	}
	else if (a[N - 1] - a[0] == 1) {
		int X = 0, Y = 0;
		for (int i = 0; i < N; i++) {
			if (a[i] == a[0]) X++;
			else Y++;
		}
		if (X < a[N - 1] && 2 * (a[N - 1] - X) <= Y) cout << "Yes";
		else cout << "No";
	}
	else cout << "No";
}