You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Given an integer $$$n$$$, you construct an array $$$a$$$ of $$$n$$$ integers, where $$$a_i = i$$$ for all integers $$$i$$$ in the range $$$[1, n]$$$. An operation on this array is defined as follows:

- Select three distinct indices $$$i$$$, $$$j$$$, and $$$k$$$ from the array, and let $$$x = a_i$$$, $$$y = a_j$$$, and $$$z = a_k$$$.
- Update the array as follows: $$$a_i = \operatorname{lcm}(y, z)$$$, $$$a_j = \operatorname{lcm}(x, z)$$$, and $$$a_k = \operatorname{lcm}(x, y)$$$, where $$$\operatorname{lcm}$$$ represents the least common multiple.

After all the operations $$$a_i \le 10^{18}$$$ should hold for all $$$1 \le i \le n$$$.

We can show that an answer always exists.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^2$$$) — the number of test cases. The description of the test cases follows.

The first and only line of each test case contains an integer $$$n$$$ ($$$3 \leq n \leq 3 \cdot 10^{4}$$$) — the length of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^{4}$$$.

## Output Format
The first line should contain an integer $$$k$$$ ($$$0 \leq k \leq \lfloor \frac{n}{6} \rfloor + 5$$$) — where $$$k$$$ is the number of operations.

The next $$$k$$$ lines should contain the description of each operation i.e. $$$3$$$ integers $$$i$$$, $$$j$$$ and $$$k$$$, where $$$1 \leq i, j, k \leq n$$$ and all must be distinct.

## Examples
```input
3
3
4
7
```
```output
1
1 2 3
1
1 3 4
3
3 5 7
5 6 7
2 3 4
```

## Note
In the third test case, $$$a = [1, 2, 3, 4, 5, 6, 7]$$$.

First operation:

$$$i = 3$$$, $$$j = 5$$$, $$$k = 7$$$

$$$x = 3$$$, $$$y = 5$$$, $$$z = 7$$$.

$$$a = [1, 2, \operatorname{lcm}(y,z), 4, \operatorname{lcm}(x,z), 6, \operatorname{lcm}(x,y)]$$$ = $$$[1, 2, \color{red}{35}, 4, \color{red}{21}, 6, \color{red}{15}]$$$.

Second operation:

$$$i = 5$$$, $$$j = 6$$$, $$$k = 7$$$

$$$x = 21$$$, $$$y = 6$$$, $$$z = 15$$$.

$$$a = [1, 2, 35, 4, \operatorname{lcm}(y,z), \operatorname{lcm}(x,z), \operatorname{lcm}(x,y)]$$$ = $$$[1, 2, 35, 4, \color{red}{30}, \color{red}{105}, \color{red}{42}]$$$.

Third operation:

$$$i = 2$$$, $$$j = 3$$$, $$$k = 4$$$

$$$x = 2$$$, $$$y = 35$$$, $$$z = 4$$$.

$$$a = [1, \operatorname{lcm}(y,z), \operatorname{lcm}(x,z), \operatorname{lcm}(x,y), 30, 105, 42]$$$ = $$$[1, \color{red}{140}, \color{red}{4}, \color{red}{70}, 30, 105, 42]$$$.

Subsequences whose GCD equal to $$$i$$$ is as follows:

$$$\gcd(a_1, a_2) = \gcd(1, 140) = 1$$$

$$$\gcd(a_3, a_4) = \gcd(4, 70) = 2$$$

$$$\gcd(a_5, a_6, a_7) = \gcd(30, 105, 42) = 3$$$

$$$\gcd(a_2, a_3) = \gcd(140, 4) = 4$$$

$$$\gcd(a_2, a_4, a_5, a_6) = \gcd(140, 70, 30, 105) = 5$$$

$$$\gcd(a_5, a_7) = \gcd(30, 42) = 6$$$

$$$\gcd(a_2, a_4, a_6, a_7) = \gcd(140, 70, 105, 42) = 7$$$

Now solve the problem and return the code.