I I U C  O N L I N E   C O N T E S T 2 0 0 8
Problem C: The 3-Regular Graph
Input: standard input Output: standard output
The degree of a vertex in a graph is the number of edges adjacent to the vertex. A graph is 3-regular if all of its vertices have degree 3. Given an integer n, you are to build a simple undirected 3-regular graph with n vertices. If there are multiple solutions, any one will do.
Input
For each test case, the input will be a single integer n as described above. End of input will be denoted by a case where n = 0. This case should not be processed.
Output
If it is possible to build a simple undirected 3-regular graph with n vertices, print a line with an integer e which is the number of edges in your graph. Each of the following e lines describes an edge of the graph. An edge description contains two integers a & b, the two endpoints of the edge. Note that the vertices are indexed from 1 to n. If it is not possible to build a simple undirected 3-regular graph with n vertices, print Impossible in a single line.
Constraints
-           1 ≤ n ≤ 100
Sample Input	Output for Sample Input
4 3 0	6 1 2 1 3 1 4 2 3 2 4 3 4 Impossible
Problem setter: Manzurur Rahman Khan Original idea: Mohammad Mahmudur Rahman