sub position {
    my($i) = @_;
    my $e = int sqrt (--$i);
    my $r = $i - $e*$e;
    if($e & 1) {  # $e is odd
        if($r <= $e) {
            $x = ($e+1)/2;
            $y = ($e-1)/2 - $r;
        } else {
            $x = ($e+1)/2 - ($r-$e);
            $y = -($e+1)/2;
        }
    } else { # $e is even
        if($r <= $e) {
            $x = -$e/2;
            $y = -$e/2 + $r;
        } else {
            $x = -$e/2 + ($r-$e);
            $y = $e/2;
        }
    }
    return ($x, $y);
}