For example, river 480 is the sequence beginning {480, 492, 507, 519, ...} and river 483 is the sequence beginning {483, 498, 519, ...}.

Normal streams and rivers can meet, and the same is true for digital rivers. This happens when two digital rivers share some of the same values. For example: river 480 meets river 483 at 519, meets river 507 at 507, and never meets river 481.

The box is a 10 by 10 grid. Each square is either empty or contains a single atom. The 36 squares on the boundary of the box, i.e. the squares adjacent to an outside edge, never contain atoms.

Rays are fired into the box from a point on the grid's edge, and can travel horizontally and vertically. Rays continue travelling in straight lines, unless affected by atoms as follows:

1. If the ray hits an atom it is absorbed (example ray 1).

2. If the ray is about to pass though a square next to an atom, it is deflected by 90 degrees away from the atom (example ray 2).

3. A ray that would pass between two atoms one square apart is reflected (example ray 3).

These rules are given in order of precedence. Note that sample ray 1 is absorbed rather than deflected.

The entry and exit points for rays will be given by a single letter followed by an integer. The letter, 'T', 'B', 'L' or 'R', indicates the side of the grid: top, bottom, left or right. The number indicates the position on the given side; for the top and bottom sides, 1 is on the left; for the left and right sides, 1 is at the bottom.

Your program should first read in 5 lines each containing two numbers; the x co-ordinate then the y co-ordinate for an atom. The bottom left corner is (1,1). You should then output the black box - using '.' for an empty square and 'A' for one containing an atom.

Until your program terminates you should repeatedly wait for input, and then:

1. If you receive 'T', 'B', 'L' or 'R' followed by an integer between 1 and 10, you should treat it as the entry point for a ray. You should display the black box, using a '+' to indicate any square the ray enters which was empty, and a '*' for any it enters that contained an atom.

   If the ray was absorbed or reflected you should output the corresponding word; otherwise you should output the exit point.

2. If you receive the input "X 0" you should terminate.

3. Ignore any other input.

Given a final score, Romulus is interested in finding the minimum number of rounds that might have taken place.

For example: 3 or 5 points are awarded at the end of each round, and Romulus finished with a score of 15. The minimum number of rounds is 3 (each scoring 5). Note that some scores, such as 4, are impossible to obtain in this case.

The first line of input will consist of a single integer n (1<=n<=10) denoting the number of possible points that can be scored in a round. The second line will consist of n integers (between 1 and 500) giving the possible points. Note that the numbers in the second line will not necessarily be sorted.

The third line of input will be a single integer m (1<=m<=10) indicating the number of final scores to be considered. The fourth line will give the m final scores to be considered (between 1 and 1,000).

Your output should consist of m lines, one for each of the final scores. Each line should contain the minimum number of rounds, followed by a corresponding example set of points. You should follow the format given in the sample run; note that the example set does not need to be sorted.

If it is not possible to produce a given score you should just output Impossible on that line.