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.