CF1355C.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.

如同任何一位不知名的数学家，尤里有他最钟爱的四个数：$A$、$B$、$C$ 和 $D$，满足 $A \leq B \leq C \leq D$。尤里也喜爱三角形，某次他想到这样一个问题：满足 $A \leq x \leq B \leq y \leq C \leq z \leq D$ 的、边长为整数 $x$、$y$、$z$ 的非退化三角形共有多少个？

尤里目前正在为一场新竞赛准备题目，因此非常忙碌。正因如此，他请你来计算满足上述条件的三角形个数。

当且仅当三角形的三个顶点不共线时，该三角形被称为非退化三角形。

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.

第一行包含四个整数：$A$、$B$、$C$ 和 $D$（$1 \leq A \leq B \leq C \leq D \leq 5 \cdot 10^5$）——尤里的最爱数字。

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.

输出满足不等式 $A \leq x \leq B \leq y \leq C \leq z \leq D$ 的非退化三角形的个数，其中三角形的边长 $x$、$y$、$z$ 均为整数。

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 $5 \cdot 10^5$.

在第一个例子中，尤里可以组成边长为 $(1, 3, 3)$、$(2, 2, 3)$、$(2, 3, 3)$ 和 $(2, 3, 4)$ 的三角形。

在第二个例子中，尤里可以组成边长为 $(1, 2, 2)$、$(2, 2, 2)$ 和 $(2, 2, 3)$ 的三角形。

在第三个例子中，尤里只能组成一个边长均为 $5 \cdot 10^5$ 的等边三角形。