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Problem 1976 Megaminx

## Problem Description

The Megaminx is made in the shape of a dodecahedron, and has 12 face center pieces, 20 corner pieces, and 30 edge pieces. The face centers each have a single color, which identifies the color of that face in the solved state. The edge pieces have two colors, and the corner pieces have three colors. Each face contains a center piece, 5 corner pieces and 5 edge pieces. The corner and edge pieces are shared with adjacent faces. The face centers can only rotate in place, but the other pieces can be permuted by twisting the face layer around the face center. It is showed in Figure 1.

Figure 1

In this problem, the start state of the Megaminx is in Figure 1 where each side of the Megaminx has a single color. According to Figure 2, all sides are numbered as follows: white '0', …, yellow ‘11’. There is a series of operations. What you need to do is to print the end state of the Megaminx after these operations. In each operation, there are two integers s and d. The first integer s indicates which side of the Megaminx should be turned.

Figure 2

The second integer d indicates in which direction the side s should be turned. The value of d is either '1' or '-1' where '1' indicates a clockwise turn and '-1' indicates a counterclockwise turn. The direction is given under the assumption that the viewer is looking directly at the specific side of the Megaminx.

Figure 3 is an example of operation “5 1”. Figure 3(1) indicates the Megaminx before the operation, and Figure 3(2) indicates the Megaminx after the operation.

Figure 3

## Input

In the first line there is an integer T (T≤50), indicating the number of cases. Each case begins with a line containing an integer number N (0≤N≤1,000), the number of the operations. Each of the following N lines contains two integers s (0≤s≤11) and d, s indicates which side of the Megaminx should be turned, d indicates which direction the side s should be turned and d can be either '1' or '-1'.

## Output

For each test case, print a line containing the test case number (beginning with 1) on its own line, then output twelve lines indicating the twelve sides according to the side numbers as said above. Each line contains eleven integers separated by a blank space indicating the color of each block. Please output the color of each block according to the block number, the block number is showed in Figure 4.

Figure 4

2 0 1 0 1

## Sample Output

Case 1: 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 Case 2: 0 0 0 0 0 0 0 0 0 0 0 5 5 5 1 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 2 2 2 3 3 3 3 2 2 2 3 3 3 3 4 4 4 4 4 4 3 3 3 4 4 4 5 5 5 5 5 5 5 4 4 5 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11

## Source

The 35th ACM/ICPC Asia Regional Fuzhou Site —— Online Contest

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