Xum

题意翻译

一开始黑板上有一个正奇数 $x\ (3\le x<10^6)$，每次你可以选定黑板上已有的正整数 $a,b$，将 $a+b$ 或 $a \oplus b$ 写在黑板上，其中 $\oplus$ 表示异或运算，最终目标是将 $1$ 写在黑板上。要求写数字不超过 $10^5$ 次且写上的数字不超过 $5*10^{18}$ 。

题目描述

You have a blackboard and initially only an odd number $ x $ is written on it. Your goal is to write the number $ 1 $ on the blackboard. You may write new numbers on the blackboard with the following two operations. - You may take two numbers (not necessarily distinct) already on the blackboard and write their sum on the blackboard. The two numbers you have chosen remain on the blackboard. - You may take two numbers (not necessarily distinct) already on the blackboard and write their [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) on the blackboard. The two numbers you have chosen remain on the blackboard. Perform a sequence of operations such that at the end the number $ 1 $ is on the blackboard.

输入输出格式

输入格式

The single line of the input contains the odd integer $ x $ ( $ 3 \le x \le 999,999 $ ).

输出格式

Print on the first line the number $ q $ of operations you perform. Then $ q $ lines should follow, each describing one operation. - The "sum" operation is described by the line " $ a $ + $ b $ ", where $ a, b $ must be integers already present on the blackboard. - The "xor" operation is described by the line " $ a $ ^ $ b $ ", where $ a, b $ must be integers already present on the blackboard. The operation symbol (+ or ^) must be separated from $ a, b $ by a whitespace.You can perform at most $ 100,000 $ operations (that is, $ q\le 100,000 $ ) and all numbers written on the blackboard must be in the range $ [0, 5\cdot10^{18}] $ . It can be proven that under such restrictions the required sequence of operations exists. You can output any suitable sequence of operations.

输入输出样例

输入样例 #1

3

输出样例 #1

5
3 + 3
3 ^ 6
3 + 5
3 + 6
8 ^ 9

输入样例 #2

123

输出样例 #2

10
123 + 123
123 ^ 246
141 + 123
246 + 123
264 ^ 369
121 + 246
367 ^ 369
30 + 30
60 + 60
120 ^ 121