You are given an m-bit binary counter, where the rightmost bit is the 1s digit, the next bit is the 2s digit, the next bit is the 4s digit, and so on, up to the 2m1 s digit. The function increment adds 1 to the counter, carrying when appropriate. Assuming that the counter starts at 0, prove that increment takes O(1) amortized time. In other words, show that after n operations, the total amount of time spent is O(n). For simplicity, assume that the only operation that takes any time is flipping a bit in the counter.