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G - GCD Permutation

Score : $600$ points

Problem Statement

Given is a permutation $P=(P_1,P_2,\ldots,P_N)$ of the integers from $1$ through $N$.

Find the number of pairs of integers $(i,j)$ such that $1\leq i\leq j\leq N$ satisfying $GCD(i,j)\neq 1$ and $GCD(P_i,P_j)\neq 1$.
Here, for positive integers $x$ and $y$, $GCD(x,y)$ denotes the greatest common divisor of $x$ and $y$.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$P_1$ $P_2$ $\ldots$ $P_N$

Output

Print the answer.

6
5 1 3 2 4 6

6

Six pairs $(3,3)$, $(3,6)$, $(4,4)$, $(4,6)$, $(5,5)$, $(6,6)$ satisfy the condition, so $6$ should be printed.

12
1 2 3 4 5 6 7 8 9 10 11 12

32