Array Pattern Generation

Background

Problem Description

Given an integer $n \ge 0$, create an array of length $n imes n$ following a specific pattern. The pattern for $n=3$ is shown as: $\{0, 0, 1, 0, 2, 1, 3, 2, 1\}$ (spaces added to show the $n$ groups).

The array can be thought of as $n$ groups, each of length $n$. Let $A$ be the array, and $A[idx]$ be its element at index $idx$.

For an element at index $idx$, let $k = \lfloor idx / n \rfloor$ be the group index (0-indexed) and $j = idx \pmod n$ be the index within the group (0-indexed).

The value of $A[idx]$ is determined as follows:

• If $j = n-1$, then $A[idx] = 1$.
• Otherwise ($j < n-1$): Let $val = n - j$. Let $min\_k = n - 1 - j$. If $k \ge min\_k$, then $A[idx] = val$. Else ($k < min\_k$), then $A[idx] = 0$.

Input Format

Input is given from standard input in the following format.

An integer $n$.

Output Format

Output is printed to standard output in the following format.

The generated array as a list of integers.

Sample

3

[0, 0, 1, 0, 2, 1, 3, 2, 1]

2

[0, 1, 2, 1]

4

[0, 0, 0, 1, 0, 0, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1]

Sample Explanation

Constraints

Time limit: 1 second, Memory limit: 1024 KiB for each test case.