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 n,i,j,a[100005],cnt[100005];

int main(){
	
	scanf("%d", &n);
	
	for(i = 0; i < n; i++){
		scanf("%d", &a[i]);
		cnt[a[i]]++;
	}
	
	sort(a, a + n);
	
	for(i = 0; i < n - 1; i++){
		if(a[i + 1] - a[i] > 1)
		return 0 * printf("No\n");
	}
	
	if(a[0] == a[n - 1]){
		if(a[0] == n - 1 || n >= 2 * a[0])
		printf("Yes\n");
		else
		printf("No\n");
	}
	else{
		if(cnt[a[0]] > a[0])
		return 0 * printf("No\n");
		
		int notunique = (a[n - 1] - cnt[a[0]]);
		
		if(cnt[a[n - 1]] >= 2 * notunique)
		printf("Yes\n");
		else
		printf("No\n");
	}
}
