N-Credible Mazes

Define an n-tersection as a point in $n$-dimensional space ($n$ a positive integer) whose coordinates are all non-negative integers. For example, $(1, 2, 3)$ is an n-tersection in three-dimensional space.

Two n-tersections are adjacent when they have the same number of dimensions and their coordinates differ by exactly $1$ in a single dimension. For example, $(1, 2, 3)$ is adjacent to $(0, 2, 3)$, $(2, 2, 3)$, and $(1, 2, 4)$, but not to $(2, 3, 3)$, $(3, 2, 3)$, or $(1, 2)$.

An n-teresting space is a collection of paths, where each path directly connects two adjacent n-tersections. An n-credible maze is an n-teresting space together with two chosen n-tersections: a start and an end.

For each maze, decide whether you can travel from the start n-tersection to the end n-tersection using only the given paths.

The input contains the descriptions of one or more mazes.

The first line of a description gives $n$, the dimension of the space ($1 \le n \le 10$, and every coordinate value is less than $10$).

The next line contains $2n$ non-negative integers: the first $n$ are the coordinates of the start n-tersection (least dimension first) and the next $n$ are the coordinates of the end n-tersection.

Then follow zero or more lines, each with $2n$ non-negative integers describing one path between two adjacent n-tersections (the first $n$ integers are one endpoint, the next $n$ are the other). This list is ended by a line containing only -1.

Several maze descriptions may appear. The input ends with a line whose dimension value is 0; no data follows that terminating zero.

For each maze, print its position in the input as Maze #k (the first maze is Maze #1, the second Maze #2, and so on). On the same line, print can be travelled if it is possible to travel through the space from the start n-tersection to the end n-tersection, or cannot be travelled if it is not.