Rin's Stone Game

Rin and his father used to play a stone game on Earth. In this game, there are n piles of stones numbered from 1 to n. In each move, Rin can remove stones in one of two ways:

• Remove a single pile i at a cost of $i \times p$.
• Remove two piles i and j at a cost of $|i-j| \times q$.

The goal is to remove all the piles with a minimum total cost. Here, p and q are given positive integers. With disaster looming, you have only 0.3 seconds to help Rin compute the answer!

inputFormat

The input consists of three space‐separated integers: n, p, and q, where n is the number of stone piles and p and q are the cost coefficients.

outputFormat

Output a single integer representing the minimum total cost required to remove all the stone piles.

sample

3 1 0

1