The Blocks Problem

Many areas of computer science use simple, abstract domains for both analytical and empirical studies. For example, an early AI study of planning and robotics (STRIPS) used a block world in which a robot arm performed tasks involving the manipulation of blocks.

In this problem, you will model a simple block world under certain rules and constraints. Rather than determine how to achieve a specified state, you will “program” a robotic arm to respond to a limited set of commands.

The problem is to parse a series of commands that instruct a robot arm in how to manipulate blocks that lie on a flat table. Initially, there are n blocks on the table (numbered from 0 to n – 1) with block b_i adjacent to block b_i + 1 for all 0 ≤ i < n – 1, as shown in the figure below:

0 1 2 3 4

…

n – 1

Initial block world

The valid commands for the robot arm that manipulates blocks are:

• move a onto b
  a and b are block numbers. Puts block a onto block b after returning any blocks that are stacked on top of blocks a and b to their initial positions.
• move a over b
  a and b are block numbers. Puts block a onto the top of the stack containing block b after returning any blocks that are stacked on top of block a to their initial positions.
• pile a onto b
  a and b are block numbers. Moves the pile of blocks consisting of block a and any blocks that are stacked above block a onto block b. All blocks on top of block b are moved to their initial positions prior to the pile taking place. The blocks stacked above block a retain their order when moved.
• pile a over b
  a and b are block numbers. Puts the pile of blocks consisting of block a and any blocks that are stacked above block a onto the top of the stack containing block b. The blocks stacked above block a retain their original order when moved.
• quit
  Terminates manipulations in the block world.

Any command in which a = b or in which a and b are in the same stack of blocks is an illegal command. All illegal commands should be ignored and should have no effect on the configuration of blocks.

Input Specification

The input begins with an integer n on a line by itself, representing the number of blocks in the block world. You may assume that 0 < n < 25.

The number of blocks is followed by a sequence of block commands, one command per line. Your program should process all commands until the quit command is encountered.

You may assume that all commands will be of the form specified above. There will be no syntactically incorrect commands.

Output Specification

The output should consist of the final state of the block world. Each original block position numbered i (0 ≤ i < n) should appear, followed immediately by a colon. If there is at least one block on it, the colon must be followed by a space, followed by a list of blocks that appear stacked in that position, with each block number separated from other block numbers by a space. Don't put any trailing spaces on a line.

There should be one line of output for each block position (i.e., a total of n lines of output).

Sample Input

1. 10
2. move 9 onto 1
3. move 8 over 1
4. move 7 over 1
5. move 6 over 1
6. pile 8 over 6
7. pile 8 over 5
8. move 2 over 1
9. move 4 over 9
10. quit

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Output for Sample Input

1. 0: 0
2. 1: 1 9 2 4
3. 2:
4. 3: 3
5. 4:
6. 5: 5 8 7 6
7. 6:
8. 7:
9. 8:
10. 9:

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