Migrated from Lutece 672 Hexagon Perplexagon

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Description

A well known puzzle consists of $7$ hexagonal pieces, each with the numbers $1$ through $6$ printed on the sides. Each piece has a different arrangement of the numbers on its sides, and the object is to place the $7$ pieces in the arrangement shown below such that the numbers on each shared edge of the arrangement are identical. Figure (a) is an example of one solution:

Input

The first line of the input file will contain a single integer indicating the number of test cases. Each case will consist of a single line containing $42$ integers. The first $6$ represent the values on piece $0$ listed in clockwise order; the second $6$ represent the values on piece $1$, and so on.

Output

For each test case, output the case number (using the format shown below) followed by either the phrase

No solution or by a solution specification. A solution specification lists the piece numbers in the order shown in the Position Notation of Figure (b). Thus if piece $3$ is in the center, a $3$ is printed first; if piece $0$ is at the top, $0$ is printed second, and so on. Each test case is guaranteed to have at most one solution.

Samples

2
3 5 6 1 2 4 5 1 2 3 6 4 2 3 5 4 1 6 3 1 5 6 2 4 5 4 1 3 6 2 4 2 3 1 5 6 3 6 1 2 4 5
6 3 4 1 2 5 6 4 3 2 5 1 6 5 3 2 4 1 5 4 6 3 2 1 2 5 6 1 4 3 4 6 3 5 2 1 1 3 5 2 6 4

Case 1: 3 0 5 6 1 4 2
Case 2: No solution

Note

Rotating any solution also gives another trivially identical solution. To avoid this redundancy, we will only deal with solutions which have a $1$ on the uppermost edge of the central piece, as in the example.

Resources

2012 East Central Regional Contest