Playing partitions

Partitions again?? Man I$\text{'}$m getting sick of these things. I$\text{'}$m sure you are too. But this

time we're going to do something a little different. We're going to play a game with

them. Or at least, we're going to study a game that could be played with them.

A position in this game is simply a Ferrers board, and a move is exactly one of the moves

described in Pathfinding partitions. The game is played by two players, who take turns

making moves. The game is defined by a starting position, and a list of target positions.

The winner is the first player to achieve one of the target positions. The game is drawn

if each player can prevent the other from achieving a target position.

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 a starting

position, and a list of target positions. The starting position will never be one of the

target positions. The output $($to stdout$)$ should be in standard form. Each scenario

should be represented by the starting position, a blank line, the list of target positions,

and then a single comment line which is one of the following:

$\frac{?}{?}$# WIN

$\frac{?}{?}$# LOSE

$\frac{?}{?}$# DRAW

indicating the outcome of the game from the starting position for the first player as$-$

suming that both players are trying to win if possible.playing partitions

Partitions are represented as a single line eg$.$

$3211$ would be

x x x

x x

x

The best approach recommended to to work on the moves backwards and go from the target to win to the starting partition and keeping track of what will be a winning position for player $1$ that goes first, what will be a losing position or a draw for both players playing the game.