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;
	cin >> N;
	vector<int> a(N);
	for (int i = 0; i < N; i++) {
		cin >> a[i];
	}
	sort(a.begin(), a.end());
	if (a.back() - a.front() >= 2) {
		cout << "No" << endl;
		return 0;
	}
	if (a.back() == a.front()) {
		cout << (a.back() == N - 1 || a.back() * 2 <= N ? "Yes" : "No") << endl;
		return 0;
	}
	int x = lower_bound(a.begin(), a.end(), a.back()) - a.begin(), y = N - x, var = a.back();
	cout << (x + 1 <= var && var <= x + y / 2 ? "Yes" : "No") << endl;
	return 0;
}
