Consider a binary counter that can increment by any power of 2, i.e. 1,2,4,8,16,... in each increment (instead of just incrementing by 1 every time). The cost of each increment is given by x^3, where x is the number of bits flipped in the increment. Show that the amortized cost of increment is O(n^2) using the potential method or otherwise.

Consider a binary counter that can increment by any power of 2, i.e. 1,2,4,8,16,... in each increment (instead of just incrementing by 1 every time). The cost of each increment is given by x^3, where x is the number of bits flipped in the increment. Show that the amortized cost of increment is O(n^2) using the potential method or otherwise.