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 <map>
using namespace std;

int N;

int main(){
	cin >> N;
	int a,mi = 1e9,ma = 0;
	map<int,int> m;
	for(int i=0;i<N;i++){
		cin >> a;
		m[a]++;
		mi = min(mi,a);
		ma = max(ma,a);
	}
	if(ma-mi>=2){
		cout << "No" << endl;
	}else if(mi==ma){
		if(ma==N-1 || m[mi]/2>=mi){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}else{
		int a = m[mi];
		if(a<ma && 2*(ma-a)<=m[ma] ){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}
}