How can I find the top three test scores + names from my array

I have completed the first two steps of my assignment as to how my teacher wanted me to, which were to: calculate and print the average score for each exam calculate and print the average score for each student, and the top scoring student

and now I can't figure out how to get it so it displays the top THREE scoring student's and their scores

I want to do this without sorting the array is ascending/descending order

My code so far is:

public class GradeBook {
public static void main(String[] args) {

    String[] names = {"Alex", "Barry","Cindy", "Deb", "Eric", "Fran", "Gary", "Helen"};

    int[][] grades = {
            { 77, 83, 96 },
            { 88, 67, 78 },
            { 92, 77, 76 },
            { 94, 42, 81 },
            { 99, 54, 72 },
            { 90, 46, 54 },
            { 76, 59, 88 },
            { 94, 69, 88 }
    };

    int rSize = grades[0].length;
    int cSize = grades.length;
    double avg = 0;
    double maxNum = 0;
    double avgSc = 0;
    ArrayList<Double> avgScores = new ArrayList();
    ArrayList topThree = new ArrayList();

    // calculate and print the average score for each exam
    for (int r = 0; r < rSize; r++) {
        avg = 0;

        for (int c = 0; c < cSize; c++) {
            avg += grades[c][r];
        }

        avg /= cSize;
        DecimalFormat a = new DecimalFormat("#.##");
        double x = Double.parseDouble(a.format(avg));

        System.out.println("\nThe average grade for Exam #" + (r+1) + ": " +x);
    }


    // calculate and print the average score for each student, and the top scoring student
    for (int c = 0; c < cSize; c++) {
        avgSc = 0;

        for (int r = 0; r < rSize; r++) {
            avgSc += grades[c][r];

        }

        avgSc /= rSize;
        DecimalFormat a = new DecimalFormat("#.##");
        double x = Double.parseDouble(a.format(avgSc));

        System.out.println("\nThe average grade for " + names[c] + ": " +x);
        avgScores.add(avgSc);

    }

    maxNum = 0;
    int topI = -1;
    for (int i = 0; i<cSize; i++) {

        if (avgScores.get(i) > maxNum){
            maxNum = avgScores.get(i);
            topI = i;
        }
        else {
            continue;
        }
    }

    DecimalFormat a = new DecimalFormat("#.##");
    double x = Double.parseDouble(a.format(maxNum));
    System.out.println("\nThe top scoring student is: " + names[topI] + ", who has an average score of: " + x);

    double top1 = 0;
    double top2 = 0;
    double top3 = 0;
    String name1 = "";
    String name2 = "";
    String name3 = "";

    // Some loop that gets the top 3 students and their scores


    }

}