题目背景

小明最近喜欢上了一个叫做"汉诺塔"的玩具，但是当老师叫小明来完成任务时，小明却在这时不知道该怎么回答老师了。

题目描述

接下来你要帮助小明完成任务。 游戏规则：

$1.要将所有的圆圈从第a个木棍到第c个木棍$

$2.一次只能拿1个$

$3.保证每个小的都在大的上面$

输入

输入一个整数$a$。

输出

输出$a$个圆圈所需的所有步骤，格式请看样例。

样例1

3

1.Move 1 from a to c
2.Move 2 from a to b
3.Move 1 from c to b
4.Move 3 from a to c
5.Move 1 from b to a
6.Move 2 from b to c
7.Move 1 from a to c

样例2

4

1.Move 1 from a to b
2.Move 2 from a to c
3.Move 1 from b to c
4.Move 3 from a to b
5.Move 1 from c to a
6.Move 2 from c to b
7.Move 1 from a to b
8.Move 4 from a to c
9.Move 1 from b to c
10.Move 2 from b to a
11.Move 1 from c to a
12.Move 3 from b to c
13.Move 1 from a to b
14.Move 2 from a to c
15.Move 1 from b to c

数据范围

$1 <= n <= 8$