Group students by grade

Summary

Organize a list of (name, grade) pairs into a dictionary mapping each grade to the sorted list of student names.

Problem statement

You are given a list of pairs (name, grade). Build and return a dictionary where each key is a grade and the corresponding value is a list of names of students who have that grade. Each list of names must be sorted alphabetically. To make tests deterministic, construct the final dictionary with its keys in ascending order (so its string representation is predictable). If the input list is empty, return an empty dictionary.

Task

Given a list of student entries, create a grouped mapping from grade to an alphabetically sorted list of students who have that grade. Ensure the resulting dictionary has keys in sorted order for deterministic representation.

Examples

Input format

A list of tuples (name: str, grade: int).

Output format

A dictionary mapping grade (int) to list of names (list of str).

Constraints

Grades are comparable (ints). Names are strings. The output dictionary must have keys inserted in sorted order for deterministic str representation.

Samples