CF388B Fox and Minimal path

Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with $ n $ vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2." Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to $ k $ ?

The first line contains a single integer $ k $ ( $ 1

You should output a graph $ G $ with $ n $ vertexes ( $ 2

In first example, there are 2 shortest paths: 1-3-2 and 1-4-2. In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.