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>
using namespace std;

int main() {
	int N;
	cin >> N;

	int arr[100000];
	int mx = 0, mn = 100000;
	for (int i = 0; i < N; ++i) {
		cin >> arr[i];
		mx = max(mx, arr[i]);
		mn = min(mn, arr[i]);
	}

	if (mn == mx) {
		if (mx == N - 1 || mx * 2 <= N) cout << "Yes";
		else cout << "No";
	}
	else if (mn + 1 == mx) {
		int x = 0, y = 0;
		for (int i = 0; i < N; ++i)
			arr[i] == mn ? ++x : ++y;

		if (x > mn) cout << "No";
		else if (mn - x + 1 <= y / 2) cout << "Yes";
		else cout << "No";
	}
	else cout << "No";

	return 0;
}
