6308: ABC230 —— G - GCD Permutation
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Description
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 $y$.
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 $y$.
Input
Input is given from Standard Input in the following format:
$N$
$P_1\ P_2\ \ldots\ P_N$
$N$
$P_1\ P_2\ \ldots\ P_N$
Output
Print the answer.
Constraints
$1≤N≤2×10^5$
$(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$.
All values in input are integers.
$(P_1,P_2,\ldots,P_N)$ is a permutation of $(1,2,\ldots,N)$.
All values in input are integers.
Sample 1 Input
6
5 1 3 2 4 6
Sample 1 Output
6
Six pairs $(3,3), (3,6), (4,4), (4,6), (5,5), (6,6)$ satisfy the condition, so $6$ should be printed.
Sample 2 Input
12
1 2 3 4 5 6 7 8 9 10 11 12
Sample 2 Output
32