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;
typedef long long ll;

const int MAXN = 1e5+5;

int n, a[MAXN];
int x, y;

int main() {
	cin >> n;
	for (int i = 0; i < n; ++i)
		cin >> a[i];
	x = n+1, y = -1;
	for (int i = 0; i < n; ++i)
		x = min(x, a[i]), y = max(y, a[i]);
	if (y-x >= 2) {
		cout << "No\n";
		return 0;
	}

	if (y == x) {
		if (x <= n/2 || x == n-1)
			cout << "Yes\n";
		else
			cout << "No\n";
		return 0;
	}

	int ctx = 0, cty = 0;
	for (int i = 0; i < n; ++i)
		ctx += (a[i] == x), cty += (a[i] == y);

	if (y <= ctx+cty/2 && y >= ctx+1)
		cout << "Yes\n";
	else
		cout << "No\n";
}