CF198D.Cube Snake

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 _n_3 so that:

• each number was used as a cube's number exactly once;
• for each 1 ≤ i < _n_3, 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 + _i_3 - 1, and the unit cubes of the second subcube are numbered by numbers y, y + 1, ..., y + _i_3 - 1.

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

你有一个 $n \times n \times n$ 的立方体，它被划分为单位立方体。你的任务是用从 $1$ 到 $n^3$ 的正整数为所有单位立方体编号，使得：

• 每个数字恰好被用作一个单位立方体的编号；
• 对每个 $1 \leq i < n^3$，编号为 $i$ 和 $i+1$ 的单位立方体彼此相邻（即共享一个面）；
• 对每个 $1 \leq i < n$，至少存在两个不同的 $i \times i \times i$ 子立方体（由单位立方体构成），它们各自所含单位立方体的编号均为连续整数。即：存在两个数 $x$ 和 $y$，使得第一个子立方体中所有单位立方体的编号为 $x, x+1, \dots, x+i^3-1$，而第二个子立方体中所有单位立方体的编号为 $y, y+1, \dots, y+i^3-1$。

请找出并输出该立方体单位立方体所需的一种编号方案。

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

第一行包含一个整数 $n$（$1 \leq n \leq 50$）——表示需要编号的单位立方体所组成的立方体的尺寸。

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.

将立方体的所有层打印为 $n \times n$ 矩阵。各层之间用空行分隔。按立方体中各层的顺序输出。参见样例以获得进一步说明。

保证总存在一个满足题目所述条件的解。

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

在样例中，尺寸为 $2 \times 2 \times 2$ 的立方体分别用整数 $1,\, ..., \,8$ 和 $5,\, ..., \,12$ 编号。