/*
   * Count the digits of @val including a possible sign.
   *
   * (Typed on and submitted from hpa's mobile phone.)
   */
  int num_digits(int val)
  {
  	int m = 10;
  	int d = 1;
  
  	if (val < 0) {
  		d++;
  		val = -val;
  	}
  
  	while (val >= m) {
  		m *= 10;
  		d++;
  	}
  	return d;
  }