$**$Question:$**$

A computer science department is developing a program to assign students to study groups based on their grades and interests. You are tasked with creating a function in Python that will:

$1.$ Accept a list of students, where each student is represented by a dictionary containing their $`$name$`,`$grade$`,$ and $`$interest$`$ fields. For example:

$```$python

students $=[$

$\{"$name$"$: "Alice", "grade": $85,$ "interest": $"$AI$"\},$

$\{"$name$"$: "Bob", "grade": $90,$ "interest": "Data Science"$\},$

$\{"$name$"$: "Charlie", "grade": $78,$ "interest": $"$AI$"\},$

$\{"$name$"$: "Diana", "grade": $92,$ "interest": "Cybersecurity"$\},$

$\{"$name$"$: "Eve", "grade": $85,$ "interest": "Data Science"$\},$

$]$

$```$

$2.$ Sort students by their $`$grade$`$ in descending order. In case of a tie in grades, further sort by their $`$interest$`$ alphabetically.

$3.$ Group students with the same grade and interest together, and return the groups as a list of lists. Each inner list should represent a unique group of students with the same grade and interest.

$**$Function Signature:$**$

$```$python

def group$\_$students$($students: list$)->$ list:

# Your code here

$```$

$**$Sample Input:$**$

$```$python

students $=[$

$\{"$name$"$: "Alice", "grade": $85,$ "interest": $"$AI$"\},$

$\{"$name$"$: "Bob", "grade": $90,$ "interest": "Data Science"$\},$

$\{"$name$"$: "Charlie", "grade": $78,$ "interest": $"$AI$"\},$

$\{"$name$"$: "Diana", "grade": $92,$ "interest": "Cybersecurity"$\},$

$\{"$name$"$: "Eve", "grade": $85,$ "interest": "Data Science"$\},$

$]$

$```$

$**$Sample Output:$**$

$```$python

$[$

$[\{"$name$"$: "Diana", "grade": $92,$ "interest": "Cybersecurity"$\}],$

$[\{"$name$"$: "Bob", "grade": $90,$ "interest": "Data Science"$\}],$

$[$

$\{"$name$"$: "Alice", "grade": $85,$ "interest": $"$AI$"\},$

$\{"$name$"$: "Eve", "grade": $85,$ "interest": "Data Science"$\},$

$],$

$[\{"$name$"$: "Charlie", "grade": $78,$ "interest": $"$AI$"\}]$

$]$

$```$

$**$Explanation:$**$

The function organizes students first by grades $($in descending order$)$ and then groups them by their interests where applicable.