Pathfinding partitions

A Ferrers board is a way of representing a partition, $(a_1,a_2,$dots,$a_k)$ as a set of rows of

dots, where the $i^{th}$ row has $a_i$ dots. For example, the partition $(5,4,3,1)$ is represented

by the following Ferrers board$*$

We could choose one of the columns of the Ferrers board, remove it$,$ and replace it with

a row of the same length as shown below.

becomes

Call such a rearrangement a move. The purpose of this $$tude is to find a sequence of

moves that will transform one partition into another, whenever this is possible.

task:

Write a program that takes input from stdin a data file formatted according to the rules

of the Parsing Partitions $$tude where each scenario in the file will consist of exactly two

partitions of the same integer.

The output $($to stdout$)$ should be in standard form and represent the solution to each

scenario, i$.$e$.,$ a shortest sequence of moves that transforms the first partition to the

second. Each scenario in the output should be in standard form and should start with

a comment line of the form:

# Moves required:

$($with a suitable replacement for $).$ This should be followed by

a sequence of lines, starting with the first partition, and ending with the last, so that

each line is obtained from the previous one by a move, and the number of moves used

is minimal. In the event that no such sequence of moves exists, the output should start

with:

# No solution possible

followed just by the two given partitions.