Minimum Cake Purchasing Cost

You are given three integers \(M\), \(C\), and \(D\) representing the number of cakes to buy, the discount per cake, and the original price of a cake, respectively.

There are two discount plans:

• Plan 1: Every third cake is free. In other words, you only pay for \(2\) out of every \(3\) cakes. The total cost under this plan is given by: \[ \text{cost}_1 = \left(\left\lfloor \frac{M}{3} \right\rfloor \times 2 + (M \bmod 3)\right) \times D \]</p>
• Plan 2: You get a discount of \(C\) yen on each cake, so the cost per cake is \(D - C\). The total cost under this plan is: \[ \text{cost}_2 = M \times (D - C) \]</p> </ul>

  Your task is to compute the minimum cost among the two plans.

  inputFormat

  The input consists of a single line containing three space-separated integers \(M\), \(C\), and \(D\).

  \(M\) is the number of cakes, \(C\) is the discount per cake, and \(D\) is the original price of a cake.

  outputFormat

  Output a single integer — the minimum total cost to purchase \(M\) cakes using the best discount plan.

  ## sample

  9 5 20

  120