Logical Sequence

Source: beecrowd

Version: Phuoc Hung OJ Extended

Problem Statement

Given integer $n$, for every $i$ from 1 to $n$ print two consecutive lines: $i$, $i^2$, $i^3$, then $i$, $i^2+1$, $i^3+1$. Separate three numbers with one space, print all digits in ordinary decimal notation.

Input

One line contains integer $n$.

Output

Print exactly $2n$ lines, keeping the two lines for each $i$ adjacent.

Subtasks

• Subtask 1 (20%): $2\le n\le 5$.

• Subtask 2 (30%): $2\le n\le 40$.

• Subtask 3 (50%): $2\le n\le 999$.

Examples

Example 1

Input:

3

Output:

1 1 1
1 2 2
2 4 8
2 5 9
3 9 27
3 10 28

Explanation:

For every i, the first line uses the square and cube; the second increases those two values by 1. For this sample, the input is 3; the displayed rows follow these rules exactly.

Example 2

Input:

2

Output:

1 1 1
1 2 2
2 4 8
2 5 9

Explanation:

For every i, the first line uses the square and cube; the second increases those two values by 1. For this sample, the input is 2; the displayed rows follow these rules exactly.