Write Python code for JPEG encoding so that the set of DC coefficients resulting from the DCT transformation of $8$x$8$ blocks are encoded using Differential Predictive Coding. The remaining DCT block coefficients should be encoded directly with Huffman coding as in the exercise. You can use any predictor you want from those tested in the exercise. Compare the compression ratio achieved with and without the Differential Predictive Coding step for the same input image.