Rectangles area

# Table: Points
# 
# +---------------+---------+
# | Column Name   | Type    |
# +---------------+---------+
# | id            | int     |
# | x_value       | int     |
# | y_value       | int     |
# +---------------+---------+
# id is the column with unique values for this table.
# Each point is represented as a 2D coordinate (x_value, y_value).
# 
#  
# 
# Write a solution to report all possible axis-aligned rectangles with a non-zero area that can be formed by any two points from the Points table.
# 
# Each row in the result should contain three columns (p1, p2, area) where:
# 
# p1 and p2 are the id's of the two points that determine the opposite corners of a rectangle.
# 
# area is the area of the rectangle and must be non-zero.
# 
# Return the result table ordered by area in descending order. If there is a tie, order them by p1 in ascending order. If there is still a tie, order them by p2 in ascending order.
# 
# The result format is in the following table.
#
# Example 1:
# Input:
# Points table:
# +----------+-------------+-------------+
# | id       | x_value     | y_value     |
# +----------+-------------+-------------+
# | 1        | 2           | 7           |
# | 2        | 4           | 8           |
# | 3        | 2           | 10          |
# +----------+-------------+-------------+
# Output:
# +----------+-------------+-------------+
# | p1       | p2          | area        |
# +----------+-------------+-------------+
# | 2        | 3           | 4           |
# | 1        | 2           | 2           |
# +----------+-------------+-------------+
# Explanation:
# The rectangle formed by p1 = 2 and p2 = 3 has an area equal to |4-2| * |8-10| = 4.
# The rectangle formed by p1 = 1 and p2 = 2 has an area equal to |2-4| * |7-8| = 2.
# Note that the rectangle formed by p1 = 1 and p2 = 3 is invalid because the area is 0.

import pandas as pd

def rectangles_area(points: pd.DataFrame) -> pd.DataFrame:
  cross = points.merge(points, how='cross', suffixes=('_1', '_2'))
  cross = cross[cross['id_1'] < cross['id_2']]
  cross['area'] = abs(cross['x_value_1'] - cross['x_value_2']) * abs(cross['y_value_1'] - cross['y_value_2'])
  cross = cross[cross['area'] > 0]
  result = cross[['id_1', 'id_2', 'area']].rename(columns={'id_1': 'p1', 'id_2': 'p2'})
  return result.sort_values(['area', 'p1', 'p2'], ascending=[False, True, True])