#include <stdio.h>

int main(int argc, char *argv[]) {
  int n, n1, a, b, c, N;

  /*  For all ints n in {0 .. N}, prints "n, (a,b)",
      where (a,b) is the n-th ordered pair of
      natural numbers under the following 
      enumeration of the ordered pairs of nat. numbers:

      <x,y> before <w,z>  iff  (x+y < w+z) or (x+y==w+z and x>w) */

  if (argc != 2) {
    printf("\n One argument--integer expected!  Exit.\n");
    return 1;
  }

  N = atoi(argv[1]);

  for (n1 = 0; n1 <= N; n1 ++) {
    n = n1;
    if (n == 0) {
      a = 0;
      b = 0;
    }
    else {
      c = 1;
      while (c <= n) {
	n = n - c;
	c ++;
      }  
      /* Now c-1 equals the # of executions of the loop's body;
         i.e., c-1 is the number of the diagonal that (a,b) is in. */
      a = c - n - 1;
      b = n;
      /* b is the offset of (a,b) in diagonal number c-1;
         a+b equals c-1. */
    }
    printf(" n = %d : (%d, %d)\n", n1, a, b);
  }

  return 0;
}