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.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \ldots P_N$

Output

Print the answer.

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.

Sample Input 1

6
5 1 3 2 4 6

Sample Output 1

6

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

Sample Input 2

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

Sample Output 2

32

见题面 Input 部分

见题面 Output 部分