A robot is moving from (0,0) according to a command sequence. Each character in the sequence is command: • L: turn left • R: turn right • F: go forward one step Interestingly, the command sequence contains some wildcard character ‘?’. The robot can treat it any one of L, R or F at its own wish, which makes it really happy. Let (x, y) be the final position of the robot, your task is to find out the minimal/maximal possible value of x and y. Initially the robot is facing east (i.e. facing (1,0) in Cartesian coordinate system). After a left turn it will face north (i.e. facing (0,1)). Input There will be at most 1000 test cases. Each case contains a command sequence with no more than 1000 characters. Output For each test case, print the case number, followed by minimal/maximal possible x (in this order), then the minimal/maximal possible y. Sample Input F?F L?? LFFFRF Sample Output Case 1: 1 3 -1 1 Case 2: -1 1 0 2 Case 3: 1 1 3 3