A326397

class A326397
{
     int initial[];
     int current[];
     int permuState[];
     int kArray[];

     A326397(int[] input){

          int initial[] = new int[input.length];
          for(int i = 0; i< initial.length; i++){
               initial[i]=input[i];
          }

          current = initial;
          permuState = new int[initial.length];
          kArray = new int[initial.length+1];
          kArray[getK(current)]++;
     }

      int getK(int a[]){
          int k=0;
          for(int i=0; i< a.length-1; i++){
               if( Math.abs(a[i]-a[i+1])==1 || Math.abs(a[i]-a[i+1])==a.length-1){
                    k++;
               }
          }
          if( Math.abs(a[0]-a[a.length-1])==1 || Math.abs(a[0]-a[a.length-1])==a.length-1){ //
               k++;
          }
          return k;
     }

    void printArray(int[] a){
        for (int i=0; i<a.length; i++)
            System.out.print(a[i]/2 + " ");
        System.out.println();
    }

     void permutate(){
          current = heapPermutation(current, permuState);
          kArray[getK(current)]++;
     }

     int[] heapPermutation(int a[], int[] permuState){
          int i = 0;
          while (i < current.length){
               if (permuState[i] < i){
                    if (i % 2 == 0){
                         int temp = a[i];
                         a[i] = a[0];
                         a[0] = temp;
                    } else {
                         int temp = a[i];
                         a[i] = a[permuState[i]];
                         a[permuState[i]] = temp;
                    }

                    permuState[i]++;
                    i = 0;
                    break;
               } else {
                    permuState[i] = 0;
                    i++;
               }
          }
          return a;
     }

    public static void main(String args[])
    {
          for(int j = 3; j< 21; j++){

               int[] sequence = new int[j];
               for(int k = 1; k<j+1;k++){
                    sequence[k-1] = k;
               }

               long iter = 1;
               for(int i=0; i< sequence.length; i++){
                    iter = iter * sequence[i];
               }
               A326397 obj = new A326397(sequence);

               for(long i = 1; i < iter; i++){
                     obj.permutate();
               }
               obj.printArray(obj.kArray);
          }
    }
}