Preparando MOJI
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.
1 2 3 4
4
1 2 2 5
3
500000 500000 500000 500000
1
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 $$$5 \cdot 10^5$$$.
Informação
Provedor Codeforces
Código CF1355C
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Datas 09/05/2023 10:02:21
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