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Robots
Description Little Y falls in love with robots recently. It's really a complex job to run a robot. So we will start with a relatively simple work. A basic problem is to handle the robot hand. The robot hand consists of N + 1 joints which are labeled from 0 to N. There's a hard rod between the kth joint and the k+1th joint. To make the problem simple, we will consider the joints and rods as N + 1 points and N segments (their thickness would be ignored in our problem) in xyz 3D (three-dimensional) coordinates. The 0th joint is always at (0, 0, 0). As the first step to handle a robot hand, Little Y needs to process some ROs (rotation operation). There are 3 parameters in RO: an integer idx in [0, N-1], a real number Alpha in [0, 2¦Ð] and a 3D non-zero vector P. With such RO, the hand from joint idx to joint N will be rotated. This part will be rotated around an axis for alpha radian. The axis is paralleled to P and passes joint idx. In our rotation, you may assume that movement will not be blocked. Now we¡¯ll explain the direction of rotations. You may easy find out your front (F), back (B), left (L), right (R), up (U) and down (D) direction. Then you may assume x-axis goes from F to B, y-axis goes from L to R and z-axis goes from D to U. For example, define 3D vectors A(1, 0, 0), B(0, 1, 0) and C(0, 0, 1) and a angle Alpha = ¦Ð⁄2. Rotate A with Alpha and axis(C) will results in B. Rotate C with Alpha and axis(B) will results in A. Rotate B with Alpha and axis(A) will results in C. Consider joint idx = (1, 1, 1), rotate (2, 1, 1) with angle = ¦Ð⁄2 and axis (0, 0, 1) will results in (1, 2, 1). However, there are so many joints and ROs for Little Y that he cannot handle them! So he asks you for help. Try to help him! Input Output Sample Input Sample Output Source |
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