Square-Free Pairs

A integer $x$ is called square-free if there is no integer $y > 1$ such that $x$ is divisible by $y^2$, that is, there is no integer $z$ with $x = y^2z$.

You are given integers $l$ and $r$. Count the pairs of integers $(a, b)$ with $l \le a < b \le r$ such that $a$, $b$, and their product $ab$ are all square-free.

The input consists of two lines. The first line contains the integer $l$, and the second line contains the integer $r$ ($1 \le l < r \le 10^9$, $r - l \le 1000$).

Print one integer, the number of pairs that satisfy the conditions.

The pairs $a = 3$, $b = 5$ and $a = 5$, $b = 6$ qualify. The number $4$ cannot be part of any pair, since $4 = 2^2\cdot 1$. The pair $a = 3$, $b = 6$ does not qualify, since $ab = 3\cdot 6 = 18 = 3^2\cdot 2$.