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;

const int N = 1e5 + 123;
int n, a[N], mx = 0, mn = 1e5 + 123, kol[N];

int main(){
	cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
		mx = max(mx, a[i]);
		mn = min(mn, a[i]);
		kol[a[i]]++;
	}
	if(mx - mn >= 2){
		cout << "No";
		exit(0);
	}
	if(mx - mn == 0){
		if(mn <= n / 2 || mn == n - 1) cout << "Yes";
		else cout << "No";
		exit(0);
	}
	else{
		if(kol[mn] <= mn && kol[mn] >= mn - (n - (mn + 2))){
			cout << "Yes";
			exit(0);
		} 
		else cout << "No";
	}
}