Xum
Description
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 on the blackboard. The two numbers you have chosen remain on the blackboard.
The single line of the input contains the odd integer $x$ ($3 \le x \le 999,999$).
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.
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.
Input
The single line of the input contains the odd integer $x$ ($3 \le x \le 999,999$).
Output
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.
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.
Samples
3
5
3 + 3
3 ^ 6
3 + 5
3 + 6
8 ^ 9
123
10
123 + 123
123 ^ 246
141 + 123
246 + 123
264 ^ 369
121 + 246
367 ^ 369
30 + 30
60 + 60
120 ^ 121