Product Triplet#1568

Product Triplet

1 second

64 megabytes

Very easy

You are given six integers: $min x$ , $ma xx$ , $min y$ , $ma x y$ , $min z$ and $ma x z$ . Find the number of triplets of integers $(x, y, z)$ (x, y, z) that satisfy the following four conditions:

$x$ is between $min x$ and $ma xx$ , inclusive;
$y$ is between $min y$ and $ma x y$ , inclusive;
$z$ is between $min z$ and $ma x z$ , inclusive;
$x \times y = z$ x \times y = z;

Input

Each line contains six integers $min x$ , $ma xx$ , $min y$ , $ma x y$ , $min z$ and $ma x z$ . It is known that $1 \leq min x \leq ma xx \leq 1 0^{9}$ 1 \leq minx \leq maxx \leq 10^9, $1 \leq min y \leq ma x y \leq 1 0^{9}$ 1 \leq miny \leq maxy \leq 10^9, $1 \leq min z \leq ma x z \leq 1 0^{9}$ 1 \leq minz \leq maxz \leq 10^9.

Output

For each line of input, print on a separate line the number of triplets $(x, y, z)$ (x, y, z) that satisfy the given conditions.

Examples

Example 1

Loading

(x, y, z)

x \times y = z

1 \leq min x \leq ma xx \leq 1 0^{9}

1 \leq min y \leq ma x y \leq 1 0^{9}

1 \leq min z \leq ma x z \leq 1 0^{9}

(x, y, z)