Balanced Food

Input

The input file contains several test cases. Each test case starts with the number of slices $n$ the pizza is cut into. Input is terminated by n = 0. Otherwise, 1 \leq n \leq 10. Then follow $9$ floating-point numbers $px$, $py$, $r$, $tx$, $ty$, $ux$, $uy$, $vx$, $vy$, specifying the coordinates of the center $p$ of the pizza, its radius, and the coordinates of three points $t$, $u$, $v$. They define the three corners of the slice-shaped table in counter-clockwise order, with $t$ being the center.

The pizza is a homogeneous two-dimensional circular object. There is always a cut from its center parallel to the $x$-axis towards increasing $x$-values. The remaining pizza stays connected during the whole process, no matter what slices are removed. The distances from $t$ to $u$, $v$ are equal except for very small rounding errors. Tables are never larger than a half-circle.

Output

For each test case output on a line the ordering of slices, so that during the whole process of eating the pizza it does not fall down from the table. Slices are numbered counter-clockwise starting with $1$ directly above the positive $x$-axis.

If several such orderings exist, choose the lexicographically first one.

If no ordering of slices exists so that the pizza does not fall down, output a line containing the word "impossible" instead.

Examples

Note

A connected, rigid, flat object remains fixed on a convex, flat surface if and only if the object's center of gravity lies above the surface. The $x$-coordinate, for example, of the center of gravity of an object $s$ can be calculated by $(...)$. Likewise, the $y$-coordinate can be expressed as $(...)$. Note that the denominator of these expressions gives the area of $s$.