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] $ .