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 su[100005];
int main(){
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		scanf("%d",&su[i]);
	}
	sort(su, su+n);
	if(su[0] == su[n-1]){
		if((su[0] == (n-1)) || su[0] <= n/2){
			printf("Yes\n");
		}else{
			printf("No\n");
		}
	}else if(su[n-1] - su[0] == 1){
		int gae = 0;
		for(int i=0;i<n;i++){
			if(su[i] != su[0]){
				gae = i;
				break;
			}
		}
		if(gae == n-1){
			printf("No\n");
		}else{
			if((((n-gae)/2) + gae < su[0]+1) || (gae > su[0]) ){
				printf("No\n");
			}else{
				printf("Yes\n");
			}
		}
	}else{
		printf("No\n");
	}
}