Ehab and a 2-operation task

1000ms

262144K

Description:

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?

Input:

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 $$$a$$$.

Output:

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.

Sample Input:

3
1 2 3

Sample Output:

Sample Input:

3
7 6 3

Sample Output:

2
1 1 1
2 2 4

Note:

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 $$$[0,2,3]$$$.

Informação

Provedor Codeforces

Código CF1088C