#!/usr/bin/perl -l

# https://perlmonks.org/?node_id=1218964

use strict;
use warnings;
use POSIX;

my $base = shift // 10;
my @numbers = (0..9, 'a'..'z')[0..$base-1];
my $numberlength = $base - 1 >> 1;
my $pattern = '-' x $numberlength . '=' . '-' x $numberlength . '*';

sub inbase
  {
  my ($n, $b) = @_;
  my $ans = '';
  while($n > 0)
    {
    $ans = $numbers[$n % $b] . $ans;
    $n = int $n / $base;
    }
  $ans || 0;
  }

# dddd=dddd*d   # for base 10

my $solutions = my $count = 0;
my @queue = map "$pattern$_", @numbers[2..$#numbers];
while( @queue )
  {
  $count++;
  $_ = shift @queue;
  /(\w).*\1/ and next;
  if( !/.*=.*\K-/ )
    {
    print;
    $solutions++;
    next;
    }
  my ($before, $after) = ($`, $');
  my $mul = POSIX::strtol( substr( $after, -1 ), $base );

  for my $d ( @numbers[1..$#numbers] )
    {
    $_ =~ $d and next;
    my $new = "$before$d$after";
    $new =~ /=-*(\w+)/ or next;;
    my $len = length $1;
    my $prod = POSIX::strtol( $1, $base ) * $mul;
    my $baseprod = inbase( $prod, $base );
    length $baseprod > $numberlength and next;

    substr $new, $numberlength - $len, $len, substr $baseprod, -$len;
    $new =~ /0|(\w).*\1/ and next;
    push @queue, $new;
    }
  }
print "\nsteps $count  solutions $solutions";