Flag An array A of size 2n that contains each integer 1, 2, . . . , n twice is balanced if, for each integer k, the two occurrences of k in A are separated by k other integers. For example, the array A = [3, 1, 2, 1, 3, 2] is balanced because there are three integers between the two 3s, two integers between the two 2s and one integer between the two 1s. This question requires you to create a python function balanced that implements an algorithm (that you must devise) that counts, for an input n, the number of balanced arrays of size 2n.