sub popnum1 {
    my( $x, $y, $z ) = @_;

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

        }
        else {
            return $aob[$x][$y] = $z + $aob[$x][ $y - 1 ];
        }
    }
}