Q$1.$ Write a Python program that takes any one of the RGB image from the given database as input, converts it to a quantized image by using $k-$Means image quantization at varying $\text{'}k\text{'}$ values i$.$c$.1,2,4,8,16.$ Also, calculates the Mean Squared Error $($MSE$).$

Your program should include the following steps:

Read an RGB image as input.

Implement a function to perform k$-$Means image quantization.

Convert the input RGB image to a quantized image using the $k-$Means algorithm by varying $"k".$

Calculate the Mean Squared Error $($MSE$)$ between the original RGB image and quantized image.

Analyze and discuss the effectiveness and limitations of $k-$Means image quantization in the context of the calculated MSE.