This is an interactive problem. There are (n) snakes on the number line. The (i)-th snake is located at the position (a_i) and has a speed (s_i). You know the position of each snake, and that the speed of each snake is an integer from (0) to (2) inclusive, but you do not know the exact speed of each snake. It is guaranteed that no two snakes are at the same position. To figure out the snakes' speed, you may give up to (3) instructions. Each instruction should be given in the form of a binary string of length (m) containing letters L and R ((1 \leq m \leq 4n)). After receiving this instruction, the snakes will move for (m) seconds. On the (i)-th second, if (s_i=) L , then all snakes move left for that second. Otherwise, all snakes move right for that second. If two snakes are at the same location at any given point (including if the time is not an integer number of seconds), the faster snake is removed from the board. After all (m) seconds have passed, you are given the number of remaining snakes, as well as the location of all remaining snakes. Note that each instruction is independent of each other – that means that all snakes are revived and moved to their original positions. Your task is to find the speed of all snakes. However, it may be the case that it is impossible to find the speed of at least one snake. If this is the case, you must report -1 instead. You should only output -1 if it is impossible to figure out the speed of at least one snake, no matter which instructions are given. If you report -1 when there are a series of at most (3) instructions that will uniquely determine the speed of each snake, you will get the Wrong Answer verdict. Similarly, you will receive the Wrong Answer verdict if you did not report -1 when the configuration is impossible to determine, even if you correctly guessed the speeds. Each test contains multiple test cases. The first line contains the number of test ca