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 a[n];
	for(int i = 0; i < n; i++) cin >> a[i];
	sort(a, a + n);
	if(1 < a[n - 1] - a[0]){
		cout << "No" << endl;
		return 0;
	}
	if(a[n - 1] - a[0] == 0) cout << (a[0] == n - 1 || a[0] <= n / 2 ? "Yes" : "No") << endl;
	else if(a[n - 1] - a[0] == 1){
		int p = 0, q = 0;
		for(int i = 0; i < n; i++) (a[i] == a[0] ? p : q)++;
		cout << (p < a[n - 1] && 2 * a[n - 1] <= 2 * p + q ? "Yes" : "No") << endl;
	}else cout << "No" << endl;
}