Problem Statement

Mitsubachi-kun has a sequence $\ A\ $ consisting of $\ N\ $ elements.
Let $A_i\ $ be the $\ i\ $-th element of $\ A\ $. Currently, $\ A_i=0\ $ holds for all integers $\ i\ $ satisfying $\ 1 \leq i \leq N\ $.

Mitsubachi-kun will now perform operations $\ Q\ $ times. The $\ i\ $-th operation is described as follows.

If $C_i=1\ $: for all integers $\ j\ $ satisfying $S_i \leq j \leq N\ $, add $\ (j-S_i+1)^2\ $ to $A_j\ $.
If $C_i=2\ $: for all integers $\ j\ $ satisfying $1 \leq j \leq S_i\ $, add $\ (S_i-j+1)^2\ $ to $A_j\ $.

After the $Q\ $ operations, Mitsubachi-kun hands you a sequence $\ B\ $ consisting of $\ N\ $ elements.
Let $B_i\ $ be the $\ i\ $-th element of $\ B\ $. Currently, $\ B_i=0\ $ holds for all integers $\ i\ $ satisfying $\ 1 \leq i \leq N\ $.

Your goal is to make $A\ $ and $\ B\ $ identical.
You may perform the following operations up to $\ 410000\ $ times in total.

Operation $\ 1$ : Choose one integer $\ i\ $ satisfying $1 \leq i \leq N\ $. Add $\ 1\ $ to $B_i\ $.
Operation $\ 2$ : Choose one integer $\ i\ $ satisfying $1 \leq i \leq N\ $. Subtract $\ 1\ $ from $B_i\ $.
Operation $\ 3$ : Choose integers $\ i,j\ $, one each, satisfying $1 \leq i,j \leq N\ $ and $\ |i-j| \leq 1\ $. Add $\ B_j\ $ to $B_i\ $.
Operation $\ 4$ : Choose integers $\ i,j\ $, one each, satisfying $1 \leq i,j \leq N\ $ and $\ |i-j| \leq 1\ $. Subtract $\ B_j\ $ from $B_i\ $.

Note that in operations $\ 3,4\ $, you may choose $\ i,j\ $ such that $\ i=j\ $.

However, since Mitsubachi-kun complains a lot, you also must not perform operations such that, during the process, there exists an integer $\ i\ $ with $\ |B_i| > 10^{17}\ $.

Under the constraints of this problem, it can be shown that there exists a way of operating that makes $\ A\ $ and $\ B\ $ identical without Mitsubachi-kun complaining, so output one.
If multiple outputs satisfy the conditions, any of them will be accepted.

Input

$N\ \ Q$
$C_1\ \ S_1$
$C_2\ \ S_2$
$\vdots$
$C_Q\ \ S_Q$

• $1 \leq N \leq 10^5$
• $1 \leq Q \leq 5 \times 10^4$
• $1 \leq C_i \leq 2(1 \leq i \leq Q)$
• $1 \leq S_i \leq N(1 \leq i \leq Q)$
• All inputs are integers

Output

On line $1\ $, output $\ X\ $, the number of operations.
As stated in the problem statement, $\ X\ $ must be an integer satisfying $\ 0 \leq X \leq 410000\ $.

Starting from line $2\ $, output the operations over $\ X\ $ lines. For each integer $\ i\ $ satisfying $2 \leq i \leq X+1\ $, the output on line $i\ $ represents the $\ i-1\ $-th operation.

For operation $\ 1\ $, output as follows.

1 i

For operation $\ 2\ $, output as follows.

2 i

For operation $\ 3\ $, output as follows.

3 i j

For operation $\ 4\ $, output as follows.

4 i j

From the above, the output consists of $\ X+1\ $ lines.
Print a newline at the end of each line of the output.

Sample

4 3
1 3
2 1
1 4

9
1 2
3 1 2
3 3 2
1 3
3 4 3
3 4 3
2 3
1 4
4 2 1

$0,0,0,0 \rightarrow 0,0,1,4 \rightarrow 1,0,1,4 \rightarrow 1,0,1,5$

$0,0,0,0 \rightarrow 0,1,0,0 \rightarrow 1,1,0,0 \rightarrow 1,1,1,0 \rightarrow 1,1,2,0 \rightarrow 1,1,2,2 \rightarrow 1,1,2,4 \rightarrow 1,1,1,4 \rightarrow 1,1,1,5 \rightarrow 1,0,1,5$