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<cstdio>
#include<algorithm>
using namespace std;
int w[101000];
int n;
int main(){
    int i;
    scanf("%d",&n);
    for(i=1;i<=n;i++)scanf("%d",&w[i]);
    sort(w+1,w+n+1);
    if(w[n]-w[1]>1){
        printf("No\n");
        return 0;
    }
    if(w[n]-w[1]==0){
        if(w[1] <= n/2 || w[1] == n-1)printf("Yes\n");
        else printf("No\n");
        return 0;
    }
    for(i=1;i<n;i++)if(w[i]!=w[i+1])break;
    int t = i;
    if(t + 1 <= w[n] && t + (n-t)/2 >= w[n])printf("Yes\n");
    else printf("No\n");
}