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
The magical girl Nene has an $$$n\times n$$$ matrix $$$a$$$ filled with zeroes. The $$$j$$$-th element of the $$$i$$$-th row of matrix $$$a$$$ is denoted as $$$a_{i, j}$$$.

She can perform operations of the following two types with this matrix:

- Type $$$1$$$ operation: choose an integer $$$i$$$ between $$$1$$$ and $$$n$$$ and a permutation $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$. Assign $$$a_{i, j}:=p_j$$$ for all $$$1 \le j \le n$$$ simultaneously.
- Type $$$2$$$ operation: choose an integer $$$i$$$ between $$$1$$$ and $$$n$$$ and a permutation $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$. Assign $$$a_{j, i}:=p_j$$$ for all $$$1 \le j \le n$$$ simultaneously.

Nene wants to maximize the sum of all the numbers in the matrix $$$\sum\limits_{i=1}^{n}\sum\limits_{j=1}^{n}a_{i,j}$$$. She asks you to find the way to perform the operations so that this sum is maximized. As she doesn't want to make too many operations, you should provide a solution with no more than $$$2n$$$ operations.

A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of test cases follows.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 500$$$) — the size of the matrix $$$a$$$.

It is guaranteed that the sum of $$$n^2$$$ over all test cases does not exceed $$$5 \cdot 10^5$$$.

## Output Format
For each test case, in the first line output two integers $$$s$$$ and $$$m$$$ ($$$0\leq m\leq 2n$$$) — the maximum sum of the numbers in the matrix and the number of operations in your solution.

In the $$$k$$$-th of the next $$$m$$$ lines output the description of the $$$k$$$-th operation:

- an integer $$$c$$$ ($$$c \in \{1, 2\}$$$) — the type of the $$$k$$$-th operation;
- an integer $$$i$$$ ($$$1 \le i \le n$$$) — the row or the column the $$$k$$$-th operation is applied to;
- a permutation $$$p_1, p_2, \ldots, p_n$$$ of integers from $$$1$$$ to $$$n$$$ — the permutation used in the $$$k$$$-th operation.

Note that you don't need to minimize the number of operations used, you only should use no more than $$$2n$$$ operations. It can be shown that the maximum possible sum can always be obtained in no more than $$$2n$$$ operations.

## Examples
```input
2
1
2
```
```output
1 1
1 1 1
7 3
1 1 1 2
1 2 1 2
2 1 1 2
```

## Note
In the first test case, the maximum sum $$$s=1$$$ can be obtained in $$$1$$$ operation by setting $$$a_{1, 1}:=1$$$.

In the second test case, the maximum sum $$$s=7$$$ can be obtained in $$$3$$$ operations as follows:

It can be shown that it is impossible to make the sum of the numbers in the matrix larger than $$$7$$$.

Now solve the problem and return the code.