Count student number in departments

# Table: Student
# 
# +--------------+---------+
# | Column Name  | Type    |
# +--------------+---------+
# | student_id   | int     |
# | student_name | varchar |
# | gender       | varchar |
# | dept_id      | int     |
# +--------------+---------+
# student_id is the primary key (column with unique values) for this table.
# dept_id is a foreign key (reference column) to dept_id in the Department tables.
# Each row of this table indicates the name of a student, their gender, and the id of their department.
# 
#  
# 
# Table: Department
# 
# +-------------+---------+
# | Column Name | Type    |
# +-------------+---------+
# | dept_id     | int     |
# | dept_name   | varchar |
# +-------------+---------+
# dept_id is the primary key (column with unique values) for this table.
# Each row of this table contains the id and the name of a department.
# 
#  
# 
# Write a solution to report the respective department name and number of students majoring in each department for all departments in the Department table (even ones with no current students).
# 
# Return the result table ordered by student_number in descending order. In case of a tie, order them by dept_name alphabetically.
# 
# The result format is in the following example.
#
# Example 1:
# Input:
# Student table:
# +------------+--------------+--------+---------+
# | student_id | student_name | gender | dept_id |
# +------------+--------------+--------+---------+
# | 1          | Jack         | M      | 1       |
# | 2          | Jane         | F      | 1       |
# | 3          | Mark         | M      | 2       |
# +------------+--------------+--------+---------+
# Department table:
# +---------+-------------+
# | dept_id | dept_name   |
# +---------+-------------+
# | 1       | Engineering |
# | 2       | Science     |
# | 3       | Law         |
# +---------+-------------+
# Output:
# +-------------+----------------+
# | dept_name   | student_number |
# +-------------+----------------+
# | Engineering | 2              |
# | Science     | 1              |
# | Law         | 0              |
# +-------------+----------------+

import pandas as pd

def count_students(student: pd.DataFrame, department: pd.DataFrame) -> pd.DataFrame:
  merged = department.merge(student, left_on='dept_id', right_on='dept_id', how='left')
  result = merged.groupby('dept_name')['student_id'].count().reset_index()
  result.columns = ['dept_name', 'student_number']
  return result.sort_values(['student_number', 'dept_name'], ascending=[False, True])