{"problem":{"name":"I. Count Triangles","description":{"content":"Like any unknown mathematician, Yuri has favourite numbers: $A$, $B$, $C$, and $D$, where $A <= B <= C <= D$. Yuri also likes triangles and once he thought: how many non-degenerate triangles with inte","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10259I"},"statements":[{"statement_type":"Markdown","content":"Like any unknown mathematician, Yuri has favourite numbers: $A$, $B$, $C$, and $D$, where $A <= B <= C <= D$. Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides $x$, $y$, and $z$ exist, such that $A <= x <= B <= y <= C <= z <= D$ holds?\n\nYuri 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.\n\nThe triangle is called non-degenerate if and only if its vertices are not collinear.\n\nThe first line contains four integers: $A$, $B$, $C$ and $D$ ($1 <= A <= B <= C <= D <= 5 dot.op 10^5$) — Yuri's favourite numbers.\n\nPrint the number of non-degenerate triangles with integer sides $x$, $y$, and $z$ such that the inequality $A <= x <= B <= y <= C <= z <= D$ holds.\n\nIn the first example Yuri can make up triangles with sides $(1, 3, 3)$, $(2, 2, 3)$, $(2, 3, 3)$ and $(2, 3, 4)$.\n\nIn the second example Yuri can make up triangles with sides $(1, 2, 2)$, $(2, 2, 2)$ and $(2, 2, 3)$.\n\nIn the third example Yuri can make up only one equilateral triangle with sides equal to $5 dot.op 10^5$.\n\n## Input\n\nThe first line contains four integers: $A$, $B$, $C$ and $D$ ($1 <= A <= B <= C <= D <= 5 dot.op 10^5$) — Yuri's favourite numbers.\n\n## Output\n\nPrint the number of non-degenerate triangles with integer sides $x$, $y$, and $z$ such that the inequality $A <= x <= B <= y <= C <= z <= D$ holds.\n\n[samples]\n\n## Note\n\nIn 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 $5 dot.op 10^5$.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ A, B, C, D \\in \\mathbb{Z} $ such that $ 1 \\leq A \\leq B \\leq C \\leq D \\leq 5 \\cdot 10^5 $.  \nLet $ x, y, z \\in \\mathbb{Z} $ be the side lengths of a triangle satisfying:  \n$$ A \\leq x \\leq B \\leq y \\leq C \\leq z \\leq D $$\n\n**Constraints**  \n1. $ x \\in [A, B] $, $ y \\in [B, C] $, $ z \\in [C, D] $  \n2. Triangle inequality: $ x + y > z $ (since $ x \\leq y \\leq z $, the other inequalities $ x + z > y $ and $ y + z > x $ are automatically satisfied)  \n\n**Objective**  \nCompute the number of integer triples $ (x, y, z) $ satisfying the above constraints and the non-degeneracy condition:  \n$$ x + y > z $$","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10259I","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}