I I U C O N L I N E C O N T E S T 2 0 0 8 

Problem C: The 3Regular 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 3regular if all of its vertices have degree 3. Given an integer n, you are to build a simple undirected 3regular 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 3regular 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 3regular 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 