Cube Snake

2000ms

262144K

Description:

You've got an n × n × n cube, split into unit cubes. Your task is to number all unit cubes in this cube with positive integers from 1 to n³ so that:

each number was used as a cube's number exactly once;
for each 1 ≤ i < n³, unit cubes with numbers i and i + 1 were neighbouring (that is, shared a side);
for each 1 ≤ i < n there were at least two different subcubes with sizes i × i × i, made from unit cubes, which are numbered with consecutive numbers. That is, there are such two numbers x and y, that the unit cubes of the first subcube are numbered by numbers x, x + 1, ..., x + i³ - 1, and the unit cubes of the second subcube are numbered by numbers y, y + 1, ..., y + i³ - 1.

Find and print the required numeration of unit cubes of the cube.

Input:

The first line contains a single integer n (1 ≤ n ≤ 50) — the size of the cube, whose unit cubes need to be numbered.

Output:

Print all layers of the cube as n n × n matrices. Separate them with new lines. Print the layers in the order in which they follow in the cube. See the samples for clarifications.

It is guaranteed that there always is a solution that meets the conditions given in the problem statement.

Sample Input:

Sample Output:

Note:

In the sample the cubes with sizes 2 × 2 × 2 are numbered with integers 1, ..., 8 and 5, ..., 12.

Informação

Provedor Codeforces

Código CF198D