Produce a program which will basically have the features of a grading system, make use of array that wait it would function along with all the covered array operations. Provide the following functions in order to satisfy the required tasks:

Function list:

1. Enlist Student: Program should able to add a student to the array provided with his/her full name and his/her average grade.
2. Search a Student: Program should be able to look for students by full name and his/her details should be displayed like this "STUDENT NAME: MARK ANTHONY CRUZ's", if not on the list display an error.
3. Update Grade: there should be a function capable of searching for a student's name and updating his grade.
4. Deleting a Student: Program should be able to remove a student by "Name"
5. Show all Students: Program should be able to display the list of students with prior numbering and remarks.

MARK ANTHONYCRUZ - 78 - "PASSED"

JOSEPH SUPANES - 59 - "FAILED"

CLERIC SANTIAGE - 89 - "PASSED"

Formula: Less than 75 is FAILED

Greater than 75 is PASSED

6. Clear List: Program should be able to remove all students on the array created.

7. Show Highest/Lowest Student: Program should be able to display either the highest or the lowest grade in the array. Show their name and their grade.

8. Show top 3: Program should be able to show the top 3 students in the array.

9. Show all students by grades (ASCENDING/DESCENDING): Program should sort and display the list of students by grades lowest to highest and highest to lowest.

10. Show summary of number failed and pass: Program should be able to display the count of students who failed and passed.