def merge$($left$,$ right$)$:

$"""$

Merges two sorted subarrays and counts inversions.

Args:

left: A sorted subarray.

right: A sorted subarray.

Returns:

A tuple containing the merged sorted array and the inversion count.

$"""$

i$,$ j$,$ count $=0,0,0$

merged $=[]$

while i $$ len$($left$)$ and j $$ len$($right$)$:

if isinstance$($left$[$i$],$ int$)$: # Check if integer array

if left$[$i right$[$j$]$:

merged.append$($left$[$i$])$

i $+=1$

else:

count $+=$ len$($left$)-$ i # Inversion occurs here

merged.append$($right$[$j$])$

j $+=1$

else: # String array, use lexicographical order

if left$[$i right$[$j$]$:

merged.append$($left$[$i$])$

i $+=1$

else:

count $+=$ len$($left$)-$ i # Inversion occurs here

merged.append$($right$[$j$])$

j $+=1$

merged $+=$ left$[$i:$]$

merged $+=$ right$[$j:$]$

return merged, count

def merge$\_$sort$($A$)$:

$"""$

Sorts an array using merge sort and counts inversions.

Args:

A: A list of comparable elements.

Returns:

A tuple containing the sorted array and the inversion count.

$"""$

if len$($A:

return A$,0$

mid $=$ len$($A$)//2$

left, left$\_$inv$\_$count $=$ merge$\_$sort$($A$[$:mid$])$

right, right$\_$inv$\_$count $=$ merge$\_$sort$($A$[$mid:$])$

merged, merge$\_$inv$\_$count $=$ merge$($left$,$ right$)$

return merged, left$\_$inv$\_$count $+$ right$\_$inv$\_$count $+$ merge$\_$inv$\_$count

def count$\_$inversions$($A$)$:

$"""$

Counts the number of inversions $($i$,$ j$)$ such that i $$ j and A$[$i$]>$ A$[$j$].$

Args:

A: A list of comparable elements.

Returns:

The total number of inversions in the array.

$"""$

sorted$\_$A$,$ inversion$\_$count $=$ merge$\_$sort$($A$)$

return inversion$\_$count

# Example usage $($integer array$)$

A $=[31,24,85,76,93,50,93]$

inversion$\_$count $=$ count$\_$inversions$($A$)$

print$("$Number of inversions $($integers$)$:$",$ inversion$\_$count$)$

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