CF1088C.Ehab and a 2-operation task

You're given an array $a$ of length $n$ . You can perform the following operations on it:

• choose an index $i$ $(1 \le i \le n)$ , an integer $x$ $(0 \le x \le 10^6)$ , and replace $a_j$ with $a_j+x$ for all $(1 \le j \le i)$ , which means add $x$ to all the elements in the prefix ending at $i$ .
• choose an index $i$ $(1 \le i \le n)$ , an integer $x$ $(1 \le x \le 10^6)$ , and replace $a_j$ with $a_j \% x$ for all $(1 \le j \le i)$ , which means replace every element in the prefix ending at $i$ with the remainder after dividing it by $x$ .

Can you make the array strictly increasing in no more than $n+1$ operations?

The first line contains an integer $n$ $(1 \le n \le 2000)$ , the number of elements in the array $a$ .

The second line contains $n$ space-separated integers $a_1$ , $a_2$ , $\dots$ , $a_n$ $(0 \le a_i \le 10^5)$ , the elements of the array $a$ .

On the first line, print the number of operations you wish to perform. On the next lines, you should print the operations.

To print an adding operation, use the format " $1$ $i$ $x$ "; to print a modding operation, use the format " $2$ $i$ $x$ ". If $i$ or $x$ don't satisfy the limitations above, or you use more than $n+1$ operations, you'll get wrong answer verdict.

In the first sample, the array is already increasing so we don't need any operations.

In the second sample:

In the first step: the array becomes $[8,6,3]$ .

In the second step: the array becomes $[0,2,3]$ .