Write a method that returns a count of Contacts grouped by Department using SOQL aggregate queries. The method should exclude Contacts with null Department values and return a Map where keys are department names and values are the count of contacts in each department.

Examples:

Map<String, Integer> departmentCounts = countContactsByDepartment();
// Returns: {'Engineering' => 5, 'Sales' => 3, 'Marketing' => 2}

Map<String, Integer> emptyCounts = countContactsByDepartment();
// Returns: {} (if no contacts have departments)