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public static int findGreatestOutlier(List<Integer> arr) {
        // Calculate the total sum of the list elements
        int totalSum = arr.stream().mapToInt(Integer::intValue).sum();
        Set<Integer> originalNumbers = new HashSet<>(arr);

        int greatestOutlier = Integer.MIN_VALUE;

        for (int num : arr) {
            // Compute the sum of the list excluding the current number
            int sumExcludingNum = totalSum - num;

            // Check if 'num' is a potential outlier
            if (!originalNumbers.contains(sumExcludingNum) && sumExcludingNum != num) {
                greatestOutlier = Math.max(greatestOutlier, num);
            }
        }

        return greatestOutlier;
    }