A13799. Xum
编程题
普及/提高-
知识点
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.
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.
- 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 #1
3
输出 #1
5 3 + 3 3 ^ 6 3 + 5 3 + 6 8 ^ 9
输入 #2
123
输出 #2
10 123 + 123 123 ^ 246 141 + 123 246 + 123 264 ^ 369 121 + 246 367 ^ 369 30 + 30 60 + 60 120 ^ 121