The first line of the input file contains a single integer t (1 ≤ t ≤ 10), the number of test cases, followed by input data for each test case describing one EE3 product. The first line of each test case is an integer n (1 ≤ n ≤ 100) which is the number of unit 4D cubes used in the product. Next, there are n lines, each describing one unit cube and contains 9 nonnegative integer numbers.
The first number, a positive integer, is the unique identifier of a cube and the remaining 8 numbers give the identities of neighbors of the cube listed in the following order:
?the first two numbers are identifiers of the cubes glued to the opposing sides of the given cube along the x1 axis as seen looking in the direction of the x1 axis;
?the next two numbers as above but for the x2 axis;
?the next two numbers as above but for the x3 axis;
?the next two numbers as above but for the x4 axis;
If a cube does not have a neighbor glued to one of its faces we use 0 instead of a cube identifier.
The problem is that the employees of ACM may produce inconsistent descriptions of EE3 products. There are two sources of such inconsistencies:
?A consistent description must be symmetric, i.e. if cube x is glued to cube y at some face then cube y must be glued to cube x at the corresponding face along the same axis. The following description is inconsistent:
3 0 0 1 0 0 0 0 0
1 0 0 3 0 0 0 0 0
?Any description must describe a single solid, i.e. there must be only one component in the product. Thus the following is inconsistent:
1 2 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0
3 0 0 4 0 0 0 0 0
4 0 0 0 3 0 0 0 0