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.