CF819E.Mister B and Flight to the Moon

In order to fly to the Moon Mister B just needs to solve the following problem.

There is a complete indirected graph with n vertices. You need to cover it with several simple cycles of length 3 and 4 so that each edge is in exactly 2 cycles.

We are sure that Mister B will solve the problem soon and will fly to the Moon. Will you?

为了飞往月球，B先生只需解决以下问题。

给定一个包含 $n$ 个顶点的完全无向图。你需要用若干个长度为 3 和 4 的简单环来覆盖该图，使得每条边恰好属于 2 个环。

我们确信 B 先生很快就能解决这个问题，并飞向月球。你呢？

The only line contains single integer n (3 ≤ n ≤ 300).

唯一的一行包含一个整数 $n$（$3 \le n \le 300$）。

If there is no answer, print -1.

Otherwise, in the first line print k (1 ≤ k ≤ _n_2) — the number of cycles in your solution.

In each of the next k lines print description of one cycle in the following format: first print integer m (3 ≤ m ≤ 4) — the length of the cycle, then print m integers _v_1, _v_2, ..., v__m (1 ≤ v__i ≤ n) — the vertices in the cycle in the traverse order. Each edge should be in exactly two cycles.

如果无解，请输出 -1。

否则，第一行输出 k（1 ≤ k ≤ n²）—— 即你所给出的解中环的数量。

接下来的 k 行中，每行描述一个环，格式如下：首先输出整数 m（3 ≤ m ≤ 4）—— 表示该环的长度，然后输出 m 个整数 v₁, v₂, ..., vₘ（1 ≤ vᵢ ≤ n）—— 表示按遍历顺序排列的环上的顶点。每条边必须恰好出现在两个环中。