Xum

Description:

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.

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.

Sample Input:

3

Sample Output:

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

Sample Input:

123

Sample Output:

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