#include <stdio.h>
#include <stdlib.h>

typedef struct {
   int a, b;
   double f;
} triple;

typedef struct {
   int size;
   triple *array;
} heap;

int gcd ( int a, int b )
{
   int r;

   if (a < 0) a = -a;
   if (b < 0) b = -b;
   if (a == 0) return b;
   if (b == 0) return a;
   while (b) {
      r = a % b;
      a = b;
      b = r;
   }
   return a;
}

heap init ( int N )
{
   heap H;
   int i;

   H.size = N;
   H.array = (triple *)malloc((N+1) * sizeof(triple));
   H.array[1].a = 0; H.array[1].b = 1; H.array[1].f = 0.0;
   for (i=2; i<=N; ++i) {
      H.array[i].a = 1; H.array[i].b = i; H.array[i].f = (double)1 / (double)i;
   }
   return H;
}

void heapify ( heap H, int i )
{
   int N, l, r, m;
   triple t;

   N = H.size;
   while (1) {
      l = 2*i; r = 2*i + 1; m = i;
      if (l > N) break;
      if (H.array[l].f < H.array[m].f) m = l;
      if ((l < N) && (H.array[r].f < H.array[m].f)) m = r;
      if (m == i) break;
      t = H.array[i]; H.array[i] = H.array[m]; H.array[m] = t;
      i = m;
   }
}

void makeheap ( heap H )
{
   int N, i;

   N = H.size;
   for (i=N/2; i>=1; --i) heapify(H,i);
}

heap insert ( heap H, triple abf )
{
   int N, i, p;
   triple t;

   N = ++(H.size);
   H.array[N] = abf;
   i = N;
   while (1) {
      if (i == 1) break;
      p = i / 2;
      if (H.array[p].f < H.array[i].f) break;
      t = H.array[i]; H.array[i] = H.array[p]; H.array[p] = t;
      i = p;
   }
   return H;
}

heap deletemin ( heap H )
{
   int N;

   N = H.size;
   H.array[1] = H.array[N];
   --(H.size);
   heapify(H,1);
   return H;
}

void sortfractions ( heap H, int N )
{
   int a, b, c;
   double f;
   char str[20];

   c = 0;
   while (H.size > 0) {
      a = H.array[1].a;
      b = H.array[1].b;
      f = H.array[1].f;
      ++c; sprintf(str, "%d / %d", a, b);
      printf("+++ Fraction No %3d : %8s = %17.15lf\n", c, str, f);
      H = deletemin(H);
      while (++a < b) {
         if (gcd(a,b) == 1) {
            f = (double)a / (double)b;
            H = insert(H,(triple){a,b,f});
            break;
         }
      }
   }
}

int main ( int argc, char *argv[] )
{
   int N;
   heap H;

   if (argc > 1) N = atoi(argv[1]); else scanf("%d", &N);
   if (N<=0) N = 10;
   printf("N = %d\n\n", N);

   H = init(N);
   makeheap(H);
   sortfractions(H,N);

   exit(0);
}