Objective: This problem will guide you through the implementation of a Python function that implements the RANSAC algorithm to perform plane fitting. Plane fitting is the process of finding the best-fit plane that passes through a set of points. RANSAC (Random Sample Consensus) is a popular algorithm used for robust plane fitting in the presence of outliers. The RANSAC function will take the following inputs: 1. points: A 3D numpy array containing the x, y, and z coordinates of the points to fit a plane to. 2. num-iterations: The number of iterations to run the RANSAC algorithm. 3. distance-threshold: The maximum distance between a point and the plane for it to be considered an inlier. 4. min-inliers: The minimum number of inliers required for a plane to be considered a good fit. Inside the function, you will: - Randomly sample 3 points from the input data. - Fit a plane to the sample using the least square fit method. - Calculate the distance between each point and the plane. - Count the number of inliers. - Update the best plane if this iteration produced a better fit. - Return the best-fit plane. Tasks (a) Using Python, load and plot the given 3D point cloud. (b) Implement a function least_sq_fit that performs the least square fit. Refer to the template for details on input/output of this function. (c) Implement RANSAC algorithm to perform robust plane fitting. The function to implement must be called plane_fit_RANSAC, with input/output as described in the template. (d) Using plane_fit_RANSAC find the plane that best fits the data. Print the coefficients a, b, c, and d for the best fit plane and plot the plane on your 3D point cloud. Choose your own values for num-iterations, distance threshold and min-inliers that achieves the best plane fit. The general equation for a plane is given by ax + by + cz + d = 0. Background RANSAC (Random Sample Consensus) is a robust algorithm used for fitting models to data in the presence of outliers. It is a popular algorithm in computer vision, robotics, and other fields where noisy or corrupt data is common. The basic idea behind RANSAC is to randomly select a subset of the input data (called a "minimal sample") and fit a model to that sample. The rest of the data is then used to evaluate the quality of the model. Points that are consistent with the model (called "inliers") are kept, while points that are not consistent with the model (called "outliers") are discarded. This process is repeated many times, with different subsets of the input data each time. The goal is to find the subset of data that contains the most inliers, which is considered to be the "best" model. Once the best model is found, it can be refined using all of the inliers. The RANSAC algorithm can be summarized in the following steps: 1. Choose a random subset of the input data (called a "minimal sample") that is just large enough to fit the model. 2. Fit the model to the minimal sample using a least-squares or other fitting method. 3. Count the number of inliers (points that are consistent with the model) based on a pre-defined