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, a[100010]; cin >> N;
	for(int i=0; i<N; ++i) cin >> a[i];
	sort(a, a+N);
	if(a[N-1]-a[0]>1) cout << "No" << endl;
	else{
	    bool flag;
	    if(a[N-1]==a[0]) flag= (2*a[0]<=N) || (a[0]+1==N);
	    else{
	        int P=1;
	        for(int i=1; a[i-1]==a[i]; ++i) ++P;
	        flag= (P<=a[0]) && ((a[0]-P+1)*2<=N-P);
	    }
	    cout << (flag ? "Yes" : "No") << endl;
	}
	return 0;
}
