#model 1;
sub popnum1 {
    ( $x, $y, $z ) = @_;

    if ( $y == 0 ) {
        $aob[$x][0] = $initial + $z;
    }
    else {
        if ( substr ($aod[ $y-1],$x,1) ne 'a' ) {
            $aob[$x][$y] = $initial + $z;
        }
        else {
            $aob[$x][$y] = $z + $aob[$x][ $y - 1 ];
        }
    }

    return $aob[$x][$y];
}