Sieve Game

Alice, after mastering the sieve of Eratosthenes, excitedly created a puzzle game that made use of it.

The rules of the puzzle game are as follows:

• An array $p_1,p_2,\ldots ,p_N$ is given where all $p_i$ is initially $0$.

• A target array $t_1,t_2,\ldots ,t_N$ is given. Her goal is to make $p_i=t_i$ for all $1\le i\le N$.

• Each time, she can perform one of the following two operations:

  • Choose $i$ and increase $p_j$ by $1$ for every $1\le j\le N$ that is a multiple of $i$.
  • Choose $i$ and decrease $p_j$ by $1$ for every $1\le j\le N$ that is a multiple of $i$.

• She can repeat this process as much as she wants.

Alice aims to solve the puzzle using the fewest operations, showcasing her puzzle-solving skill. Please help Alice find the minimum number of operations to solve the puzzle.

The first line contains one integer, $N$.

The second line contains space-separated $N$ integers — elements of the array $t$.

Print out the minimum number of operations to solve the puzzle. If the puzzle is unsolvable, print -1.

• $1\le N\le 200\, 000$
• $-10^9\le t_i\le 10^9\ (1\le i\le N)$
• All values in the input are integers.