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E. Mister B and Flight to the Moon

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn 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?

Input

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

Output

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.

Examples

Input

3

Output

2

3 1 2 3

3 1 2 3

Input

5

Output

6

3 5 4 2

3 3 1 5

4 4 5 2 3

4 4 3 2 1

3 4 2 1

3 3 1 5

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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