
ZOJ Problem Set  3736
Pocket Cube is a 3D combination puzzle. It is a 2 × 2 × 2 cube, which means it is constructed by 8 minicubes. For a combination of 2 × 2 minicubes which sharing a whole cube face, you can twist it 90 degrees in clockwise or counterclockwise direction, this twist operation is called one twist step. Considering all faces of minicubes, there will be totally 24 faces painted in 6 different colors (Indexed from 0), and there will be exactly 4 faces painted in each kind of color. If 4 minicubes' faces of same color rely on same large cube face, we can call the large cube face as a completed face. Now giving you an color arrangement of all 24 faces from a scrambled Pocket Cube, please tell us the maximum possible number of completed faces in no more than N twist steps. Index of each face is shown as below: InputThere will be several test cases. In each test case, there will be 2 lines. One integer N (1 ≤ N ≤ 7) in the first line, then 24 integers C_{i} seperated by a sinle space in the second line. For index 0 ≤ i < 24, C_{i} is color of the corresponding face. We guarantee that the color arrangement is a valid state which can be achieved by doing a finite number of twist steps from an initial cube whose all 6 large cube faces are completed faces. OutputFor each test case, please output the maximum number of completed faces during no more than N twist step(s). Sample Input1 0 0 0 0 1 1 2 2 3 3 1 1 2 2 3 3 4 4 4 4 5 5 5 5 1 0 4 0 4 1 1 2 5 3 3 1 1 2 5 3 3 4 0 4 0 5 2 5 2 Sample Output6 2 Author: FAN, Yuzhe;CHEN, Cong;GUAN, Yao Contest: The 2013 ACMICPC Asia Changsha Regional Contest 