Ehab and a 2-operation task

# 题目描述 有一个长度为$n$的序列$a$,你可以在这个序列上做两种操作: + 选择下标 $i(1 \leq i \leq n) $ 和一个整数$x(0 \leq x \leq 10^6)$,然后对每一个下标$j(1 \leq j \leq i)$,把所有的$a_j$换成$a_j+x$,也就是说,给序列中以$i$为最后一个元素的前缀中的每一个元素加上$x$. + 选择一个下标$i,(1 \leq i \leq n) $,一个整数$x(0 \leq x \leq 10^6)$,然后对每一个下标$j(1 \leq j \leq i)$,把$a_j$换成 $a_j \% s$,也就是说，把序列中以$i$为最后一个元素的前缀中的每一个元素对$x$取模. 你能在不超过$n+1$次操作之内把这个序列变成严格递增的吗? # 输入输出格式 ## 输入格式： 第一行有一个整数$n(1\leq n \leq 1000)$,代表$a$中元素的个数. 第二行有n个以空格间隔的整数:$a_1,a_2,...,a_n$,$(0 \leq a_i\leq 10^5)$,是序列$a$中的元素. ## 输出格式： 第一行输出你要进行的操作个数. 接下来的每一行,你需要依次输出每一个操作. 要输出添加操作的时候,用"1 i x"(没有引号)的格式;要输出取模操作时,用"2 i x"(没有引号)的格式. 如果$i$或者$x$没有满足题目中的限制,或者你用了超过$n+1$次操作,你的提交就会被认为是错误的。

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.

3
1 2 3

0

3
7 6 3

2
1 1 1
2 2 4

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] $ .