{"problem":{"name":"B. Magic Forest","description":{"content":"Imp is in a magic forest, where xorangles grow (wut?)
![image](https://espresso.codeforces.com/41a89e297f110aa906c319b9c9c581669469c1f7.png)
A xorangle of order _n_ is such a non-dege","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF922B"},"statements":[{"statement_type":"Markdown","content":"Imp is in a magic forest, where xorangles grow (wut?)\n\n
![image](https://espresso.codeforces.com/41a89e297f110aa906c319b9c9c581669469c1f7.png)
A xorangle of order _n_ is such a non-degenerate triangle, that lengths of its sides are integers not exceeding _n_, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order _n_ to get out of the forest.\n\nFormally, for a given integer _n_ you have to find the number of such triples (_a_, _b_, _c_), that:\n\n* 1 ≤ _a_ ≤ _b_ ≤ _c_ ≤ _n_;\n* , where denotes the [bitwise xor](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of integers _x_ and _y_.\n* (_a_, _b_, _c_) form a non-degenerate (with strictly positive area) triangle.\n\n## Input\n\nThe only line contains a single integer _n_ (1 ≤ _n_ ≤ 2500).\n\n## Output\n\nPrint the number of xorangles of order _n_.\n\n[samples]\n\n## Note\n\nThe only xorangle in the first sample is (3, 5, 6).","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"Imp 在一个魔法森林中，那里生长着 xorangles（什么？）\n\n一个阶为 #cf_span[n] 的 xorangle 是指一个非退化三角形，其三边长度为不超过 #cf_span[n] 的整数，且三边长度的交错和等于零。Imp 需要计算阶为 #cf_span[n] 的不同 xorangle 的数量，才能走出这片森林。\n\n形式化地，给定整数 #cf_span[n]，你需要找出满足以下条件的三元组 #cf_span[(a, b, c)] 的数量：\n\n输入仅包含一行，一个整数 #cf_span[n] #cf_span[(1 ≤ n ≤ 2500)]。\n\n请输出阶为 #cf_span[n] 的 xorangle 的数量。\n\n第一个样例中唯一的 xorangle 是 #cf_span[(3, 5, 6)]。\n\n## Input\n\n输入仅包含一行，一个整数 #cf_span[n] #cf_span[(1 ≤ n ≤ 2500)]。\n\n## Output\n\n请输出阶为 #cf_span[n] 的 xorangle 的数量。\n\n[samples]\n\n## Note\n\n第一个样例中唯一的 xorangle 是 #cf_span[(3, 5, 6)]。","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions** \nLet $ n \\in \\mathbb{Z} $ with $ 1 \\leq n \\leq 2500 $. \nA *xorangle of order $ n $* is a triple $ (a, b, c) \\in \\mathbb{Z}^3 $ such that: \n- $ 1 \\leq a \\leq b \\leq c \\leq n $, \n- $ a \\oplus b \\oplus c = 0 $, \n- $ a + b > c $ (non-degenerate triangle condition). \n\n**Constraints** \n$ 1 \\leq n \\leq 2500 $\n\n**Objective** \nCount the number of distinct triples $ (a, b, c) $ satisfying the above conditions.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF922B","tags":["brute force"],"sample_group":[["6","1"],["10","2"]],"created_at":"2026-03-03 11:00:39"}}