Array GCD

You are given an array of $N$ integers $a_1, a_2, \dots, a_N$. You can apply two kinds of operations to this array.

1. Delete a contiguous block of length $m$ from the array.
2. Add 1 to a number $a_i$ in the array, or subtract 1 from it.

Operation 1 can be used at most once in total, and operation 2 can be used at most once on each number. When you use operation 1, $1 \le m < N$ must hold, so you cannot delete the whole array.

Operation 1 costs $m \times A$, and each use of operation 2 costs $B$. After every operation is done, the greatest common divisor of the remaining array has to be greater than 1. Write a program that finds the minimum cost needed for this.

The first line contains $N$, $A$, and $B$. ($1 \le N \le 1\,000\,000$, $1 \le A, B \le 10^9$)

The second line contains the numbers in the array, $a_1, a_2, \dots, a_N$. ($2 \le a_i \le 10^9$)

Print the minimum cost that makes the greatest common divisor of the array greater than 1 on the first line.

In the first example, deleting the third number with operation 1 gives the minimum cost.

In the second example, deleting the second number through the third number with operation 1 and then lowering the fifth number by 1 with operation 2 gives the minimum cost.