A complete graph is a graph in which each pair of vertices is joined by an undirected edge and there's no self-loop or multiple edges. Given a complete graph with  vertices numbered from to . You can delete the edges in the graph several times. Each time you need to choose  vertices  under the condition that the edges  are not deleted, then delete these  edges.

You need to find a solution to make the number of the rest edges less than .

输入描述:

An integer  () --- the number of vertices in the complete graph.

输出描述:

The first line contains an integer  --- the number of times you delete edges.
In the next  lines, each line contains three integers  --- the vertices you choose each time.

If there are multiple solutions, print any of them. Note that you just need to make the number of the rest edges less than . You don't need to minimize the number.

3

1
1 2 3