sub popnum3 {
    my ( $x, $y, $z ) = @_;  # $_[3] is $zazb
    if ( $y == 0 ) {
        $aob[$x][0] = $initial * ( 1 + $z );
    }
    else {
        my @cPosns;
        push @cPosns, $-[0] while $_[3] =~ m{c}g;
        if (@cPosns) {
            my $offset = $cPosns[rand @cPosns];
            $aob[$x][$y] = $aob[$offset][ $y - 1 ] * ( 1 + $z );
        }
    }
    return $aob[$x][$y];
}