Beautiful Array

You're given an array $A$ of $N$ integers. You need to find the minimum cost of creating another array $B$ of $N$ integers with the following properties - $B_i \ge 0$ for each $1 \leq i \leq N$ - The GCD of adjacent elements of $B$ is equal to $1$, i.e, $\gcd(B_i, B_{i+1}) = 1$ for each $1 \leq i \lt N$ The cost of creating $B$ is defined as follows: $$ \sum_{i=1}^{N} 2^{|A_i - B_i |} $$ Find