[OA][TLE] Find sum of all Happy Numbers in a range [L,R]

Problem: Given a range [L,R], find sum of all happy numbers in it.
A Happy number is: https://leetcode.com/problems/happy-number/

I have tried with below method and got TLE.

Any help is highly appreciated. I have encountered this question in more than 1 OAs.

    private static Set<Integer> cycleMembers =
            new HashSet<>(Arrays.asList(4, 16, 37, 58, 89, 145, 42, 20));
    private static Set<Integer> nonCycleMembers =
            new HashSet<>();

    public static int  getNext(int n) {
        int totalSum = 0;
        while (n > 0) {
            int d = n % 10;
            n = n / 10;
            totalSum += d * d;
        }
        return totalSum;
    }


    public static boolean isHappy(int n) {
        Set<Integer> set = new HashSet<>();
        while (n != 1 && !cycleMembers.contains(n)) {
            set.add(n);
            n = getNext(n);
            if(nonCycleMembers.contains(n)) return true;
        }
        if(n==1) {
            nonCycleMembers.addAll(set);
        } else {
            cycleMembers.addAll(set);
        }
        return n == 1;
    }

    static long solve(int l, int r) {
        long result = 0;

        for(int i=l;i<=r;i++) {
            if(nonCycleMembers.contains(i) || isHappy(i)) {
                result += i;
            }
        }

        return result;
    }
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