103351: [Atcoder]ABC335 B - Tetrahedral Number

Problem Statement

You are given an integer $N$.

Print all triples of non-negative integers $(x,y,z)$ such that $x+y+z\leq N$ in ascending lexicographical order.

Constraints

• $0 \leq N \leq 21$
• $N$ is an integer.

Input

The input is given from Standard Input in the following format:

$N$

Output

Print all triples of non-negative integers $(x,y,z)$ such that $x+y+z\leq N$ in ascending lexicographical order, with $x,y,z$ separated by spaces, one triple per line.

Sample Input 1

3

Sample Output 1

0 0 0
0 0 1
0 0 2
0 0 3
0 1 0
0 1 1
0 1 2
0 2 0
0 2 1
0 3 0
1 0 0
1 0 1
1 0 2
1 1 0
1 1 1
1 2 0
2 0 0
2 0 1
2 1 0
3 0 0

Sample Input 2

4

Sample Output 2

0 0 0
0 0 1
0 0 2
0 0 3
0 0 4
0 1 0
0 1 1
0 1 2
0 1 3
0 2 0
0 2 1
0 2 2
0 3 0
0 3 1
0 4 0
1 0 0
1 0 1
1 0 2
1 0 3
1 1 0
1 1 1
1 1 2
1 2 0
1 2 1
1 3 0
2 0 0
2 0 1
2 0 2
2 1 0
2 1 1
2 2 0
3 0 0
3 0 1
3 1 0
4 0 0

问题描述

你将得到一个整数$N$。

按字典序递增顺序打印出所有满足$x+y+z\leq N$的非负整数三元组$(x,y,z)$。

限制条件

• $0 \leq N \leq 21$
• $N$是一个整数。

输入

输入以标准输入的形式给出，如下所示：

$N$

输出

按字典序递增顺序打印出所有满足$x+y+z\leq N$的非负整数三元组$(x,y,z)$，用空格分隔$x,y,z$，每行一个三元组。

样例输入1

3

样例输出1

0 0 0
0 0 1
0 0 2
0 0 3
0 1 0
0 1 1
0 1 2
0 2 0
0 2 1
0 3 0
1 0 0
1 0 1
1 0 2
1 1 0
1 1 1
1 2 0
2 0 0
2 0 1
2 1 0
3 0 0

样例输入2

4

样例输出2

0 0 0
0 0 1
0 0 2
0 0 3
0 0 4
0 1 0
0 1 1
0 1 2
0 1 3
0 2 0
0 2 1
0 2 2
0 3 0
0 3 1
0 4 0
1 0 0
1 0 1
1 0 2
1 0 3
1 1 0
1 1 1
1 1 2
1 2 0
1 2 1
1 3 0
2 0 0
2 0 1
2 0 2
2 1 0
2 1 1
2 2 0
3 0 0
3 0 1
3 1 0
4 0 0