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Explan

• Cooking the perfect stack of pancakes on a grill is a tricky business, because no matter how hard you try all pancakes in any stack have different diameters.
• For neatness’s sake, however, you can sort the stack by size such that each pancake is smaller than all the pancakes below it.
• The size of pancake is given by its diameter.
• Sorting a stack is done by a sequence of pancake “flips.”
• A flip consists of inserting a spatula between two pancakes in a stack and flipping(reversing) all the pancakes on the spatula (reversing the sub-stack).
• A flip is specified by giving the position of the pancake on the bottom of the sub-stack to be flipped relative to the entire stack.
• The bottom pancake has position 1, while the top pancake on a stack of n pancakes has position n.
• A stack is specified by giving the diameter of each pancake in the stack in the order in which the pancakes appear.

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Example

• The stack on the left can be transformed to the stack in the middle via flip(3).
• The middle stack can be transformed into the right stack via the command flip(1).

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Input

1 2 3 4 5
5 4 3 2 1
5 1 2 3 4
3 5 2 1 7 6 4

• The input consist of a sequence of stacks of pancakes.
• Each stack will consist of between 1 and 30 pancakes and each pancake will have an integer diameter between 1 and 10.
• The input is terminated by end-of-file.
• Each stack is given as a single line of input with the top pancake on a stack appearing first on a line, the bottom pancake appearing last, and all pancakes separated by a space.

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Output

1 2 3 4 5
0
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1 2 3 4 5
1 0
----------------
1 2 3 4 5
1 2 0
----------------
1 2 3 4 5 6 7
3 1 6 2 5 3 4 6 0

• For each stack of pancakes, your program should echo the original stack on one line, followed by a sequence of flips that results in sorting the stack of pancakes so that the largest pancake is on the bottom and the smallest on top.
• The sequence of flips for each stack should be terminated by a 0, indicating no more flips necessary.
• Once a stack is sorted, no more flips should be made.