Please write the complete Python code for the method below:

def perform$\_$exact$\_$inference$($model: BeliefNetwork, Q:Variable, E: Dict$[$Variable$,$ int$],$ ordering: List$[$Variable$])->$ Dict$[$int$,$ float$]$:

$"""$ Computes P$($Q $|$ E$)$ on a Bayesian Network using variable elimination

Arguments:

model, the Bayesian Network

Q$,$ the query variable

E$,$ the evidence

ordering, the order in which variables are eliminated

Returns

result, a dict mapping each possible value $($q$)$ of Q to the probability P$($Q $=$ q $|$ E$)$

$"""$

# Use the VE class to perform variable elimination

pass

This comes from the question below that needs to be solved:

Part $1$: Exact Inference

In this part, you will load the BN from the JSON files and perform exact inference on it using the Variable Elimination algorithm.

$1.$ Construct an instance of the BeliefNetwork class. Refer hw$\_$example.py for an example.

$2.$ Implement the perform$\_$exact$\_$inference function. The function computes the query P$($Q $|$ E$)$ on a given BN using the Variable elimination algorithm. It eliminates variables in the order specified by the ordering parameter.

$3.$ Use the perform$\_$exact$\_$inference function to compute P$($Disease $|$ CO$2$Report $=1,$ XrayReport $=0,$ Age $=0)$

a$.$ Set ordering to be alphabetical order of the variable names

b$.$ Use a better ordering. You may ask an LLM$.$

$4.$ Use the timeit module to compute the average time taken over $10$ runs by both approaches..

Save it as a csv file named $$part$1.$csv$$ containing exactly one row and two values

representing the time taken by each method.