## Problem: Stacks of Flapjacks

### Background

Stacks and Queues are often considered the bread and butter of data
structures and find use in architecture, parsing, operating systems, and
discrete event simulation. Stacks are also important in the theory of
formal languages.
This problem involves both butter and sustenance in the form of pancakes
rather than bread in addition to a finicky server who flips pancakes
according to a unique, but complete set of rules.

### The Problem

Given a stack of pancakes, you are to write a program that indicates how
the stack can be sorted so that the largest pancake is on the bottom
and the smallest pancake is on the top. The size of a pancake is given
by the pancake's diameter. All pancakes in a stack have different
diameters.
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 whole stack). The pancake
on the bottom of the whole stack has position 1 and the pancake on the
top of 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.

For example, consider the three stacks of pancakes below
(in which pancake 8 is the top-most pancake of the left stack):

8 7 2
4 6 5
6 4 8
7 8 4
5 5 6
2 2 7

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) *.
### The Input

The input consists 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 100. 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.

### The Output

For each stack of pancakes, the output should echo the original stack on
one line, followed by some sequence of flips that results in the stack
of pancakes being sorted so that the largest diameter pancake is on the
bottom and the smallest on top. For each stack the sequence of flips
should be terminated by a 0 (indicating no more flips necessary). Once
a stack is sorted, no more flips should be made.
** Sample Input **

1 2 3 4 5
5 4 3 2 1
5 1 2 3 4

** Sample Output **
1 2 3 4 5
0
5 4 3 2 1
1 0
5 1 2 3 4
1 2 0