A13561. Count Triangles

Like any unknown mathematician, Yuri has favourite numbers: $A$ , $B$ , $C$ , and $D$ , where $A \leq B \leq C \leq D$ . Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides $x$ , $y$ , and $z$ exist, such that $A \leq x \leq B \leq y \leq C \leq z \leq D$ holds?

Yuri is preparing problems for a new contest now, so he is very busy. That's why he asked you to calculate the number of triangles with described property.

The triangle is called non-degenerate if and only if its vertices are not collinear.

The first line contains four integers: $A$ , $B$ , $C$ and $D$ ( $1 \leq A \leq B \leq C \leq D \leq 5 \cdot 10^5$ ) — Yuri's favourite numbers.

Print the number of non-degenerate triangles with integer sides $x$ , $y$ , and $z$ such that the inequality $A \leq x \leq B \leq y \leq C \leq z \leq D$ holds.

In the first example Yuri can make up triangles with sides $(1, 3, 3)$ , $(2, 2, 3)$ , $(2, 3, 3)$ and $(2, 3, 4)$ .

In the second example Yuri can make up triangles with sides $(1, 2, 2)$ , $(2, 2, 2)$ and $(2, 2, 3)$ .

In the third example Yuri can make up only one equilateral triangle with sides equal to $5 \cdot 10^5$ .