A13799 | Xum

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.

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.

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.