Break up the following one dimensional data into 2 and 4 clusters, and calculate their inner and outer distances for each cluster/cluster pair using center-wise and border-wise methods respectively

Your clusters should satisfy the minimum inner and maximum outer distances objectives for each number of clusters.

What would be the ideal number of clusters, where we reach to the optimum in both distances? Discuss/justify your answer. Remember that 1 < #of clusters < # of items (data size). Code Implementation is required

Data: 18, 20, 19, 2, 1, 10, 7, 9, 12, 14, 16, 15