| Standard mazes lose their mystery as one grows older. But throw in some | |
| lasers, and suddenly you've got yourself a recipe for cross-generational | |
| appeal. The object in any maze is to find your way from your starting point to | |
| some goal. In a _Laser Maze_ you must additionally contend with laser turrets. | |
| A laser turret is a stationary pillar that both blocks your movement and fires | |
| lasers from one side. Every time you take a step (either up, down, left, or | |
| right), every laser turret in the maze then rotates 90 degrees clockwise, and | |
| then shoots a momentary laser blast in the direction that it is facing. | |
| Needless to say, if you find yourself in the path of one of these lasers, you | |
| won't be around long enough to find a way out. A wall is a stationary pillar | |
| that blocks your movement, but does not fire lasers. | |
| Lasers are powerful, but they do not pass through walls or laser turrets. The | |
| laser turrets respond to your movements, so you can't stand still and wait for | |
| the turrets to turn. If you reach the goal, but are immediately shot by a | |
| laser, your efforts will have been in vain, so make sure you reach the goal | |
| safely. | |
| ### Input | |
| Input begins with an integer **T**, the number of mazes you'll explore. For | |
| each maze, there is first a line containing two integers, **M** and **N**, the | |
| height and width of the maze, respectively. The next **M** lines contain **N** | |
| characters each, describing the maze: | |
| . (empty space) | |
| # (wall) | |
| S (starting position) | |
| G (goal) | |
| < > ^ v (laser turrets) | |
| The four symbols for laser turrets signify turrets that are initially pointing | |
| left, right, up, or down respectively before you take your first step. | |
| ### Output | |
| For the _i_th maze, print a line containing "Case #_i_: " followed by the | |
| smallest number of steps necessary to get to the exit without being hit by a | |
| laser, or the string "impossible'' if there is no way to reach the goal | |
| safely. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 100 | |
| 1 ≤ **M**, **N** ≤ 100 | |
| Each maze will contain exactly one 'S' and exactly one 'G'. | |