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>

using namespace std;

int main()
{
	ios::sync_with_stdio(false);
	int n, maxx = 0, minn = 233333333, cnt = 0;
	cin >> n;
	for (int i = 1, x; i <= n; ++i)
	{
		cin >> x;
		if (x < minn)
			cnt = 0;
		maxx = max(maxx, x);
		minn = min(minn, x);
		if (x == minn)
			cnt++;
	}
	if (maxx - minn > 1)
		cout << "No";
	else if (maxx == minn)
		cout << ((maxx == n - 1 || maxx <= (n >> 1)) ? "Yes" : "No");
	else
		cout << ((cnt < maxx && maxx <= (cnt + ((n - cnt) >> 1))) ? "Yes" : "No");
	return 0;
}