This function works but is O(n³). Optimize it to O(n log n) or better while maintaining correctness. ```python def find_triplets_with_sum(arr, target_sum): """Find all unique triplets in arr that sum to target_sum""" n = len(arr) result = [] for i in range(n): for j in range(i + 1, n): for k in range(j + 1, n): if arr[i] + arr[j] + arr[k] == target_sum: triplet = sorted([arr[i], arr[j], arr[k]]) if triplet not in result: result.append(triplet) return result ``` Explain your optimization approach and prove the new time complexity.