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;
int main(){
	int N; 
	cin >> N; 
	int A[100010] = {}; 
	int B[100010] = {}; 
	int mn = N, mx = 0; 
	for(int i = 0; i < N; i++){
		cin >> A[i]; 
		mn = min(mn, A[i]), mx = max(mx, A[i]); 
		B[A[i]] ++; 
	}
	if(mx - mn >= 2) cout << "No" << endl; 
	else if(mx == mn){
		if(N == mx + 1 || N >= mx * 2) cout << "Yes" << endl; 
		else cout << "No" << endl; 
	}
	else{
		if(B[mx] >= 2 * (mx + B[mx] - N) && mx + B[mx] - N > 0) cout << "Yes" << endl; 
		else cout << "No" << endl; 
	}
}