{"problem":{"name":"B. Makes And The Product","description":{"content":"After returning from the army Makes received a gift — an array _a_ consisting of _n_ positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a part","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF817B"},"statements":[{"statement_type":"Markdown","content":"After returning from the army Makes received a gift — an array _a_ consisting of _n_ positive integer numbers. He hadn't been solving problems for a long time, so he became interested to answer a particular question: how many triples of indices (_i_,  _j_,  _k_) (_i_ < _j_ < _k_), such that _a__i_·_a__j_·_a__k_ is minimum possible, are there in the array? Help him with it!\n\n## Input\n\nThe first line of input contains a positive integer number _n_ (3 ≤ _n_ ≤ 105) — the number of elements in array _a_. The second line contains _n_ positive integer numbers _a__i_ (1 ≤ _a__i_ ≤ 109) — the elements of a given array.\n\n## Output\n\nPrint one number — the quantity of triples (_i_,  _j_,  _k_) such that _i_,  _j_ and _k_ are pairwise distinct and _a__i_·_a__j_·_a__k_ is minimum possible.\n\n[samples]\n\n## Note\n\nIn the first example Makes always chooses three ones out of four, and the number of ways to choose them is 4.\n\nIn the second example a triple of numbers (1, 2, 3) is chosen (numbers, not indices). Since there are two ways to choose an element 3, then the answer is 2.\n\nIn the third example a triple of numbers (1, 1, 2) is chosen, and there's only one way to choose indices.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"[{\"iden\":\"statement\",\"content\":\"在从军队归来后，Makes 收到一份礼物——一个由 #cf_span[n] 个正整数组成的数组 #cf_span[a]。由于长时间没有解题，他开始对一个问题产生兴趣：有多少个三元组索引 #cf_span[(i,  j,  k)]（#cf_span[i < j < k]），使得 #cf_span[ai·aj·ak] 达到最小可能值？请帮助他解决这个问题！\\n\\n输入的第一行包含一个正整数 #cf_span[n (3 ≤ n ≤ 105)] —— 数组 #cf_span[a] 中的元素个数。第二行包含 #cf_span[n] 个正整数 #cf_span[ai (1 ≤ ai ≤ 109)] —— 给定数组的元素。\\n\\n输出一个数字——满足 #cf_span[i,  j] 和 #cf_span[k] 互不相同且 #cf_span[ai·aj·ak] 达到最小可能值的三元组 #cf_span[(i,  j,  k)] 的数量。\\n\\n在第一个例子中，Makes 总是从四个 1 中选出三个，选择它们的方式数为 #cf_span[4]。\\n\\n在第二个例子中，选择的三元组是数字 #cf_span[(1, 2, 3)]（指数字，而非索引）。由于有两种方式选择元素 #cf_span[3]，因此答案为 #cf_span[2]。\\n\\n在第三个例子中，选择的三元组是数字 #cf_span[(1, 1, 2)]，且只有一种方式选择索引。\"}},{\"iden\":\"input\",\"content\":\"输入的第一行包含一个正整数 #cf_span[n (3 ≤ n ≤ 105)] —— 数组 #cf_span[a] 中的元素个数。第二行包含 #cf_span[n] 个正整数 #cf_span[ai (1 ≤ ai ≤ 109)] —— 给定数组的元素。\"},{\"iden\":\"output\",\"content\":\"输出一个数字——满足 #cf_span[i,  j] 和 #cf_span[k] 互不相同且 #cf_span[ai·aj·ak] 达到最小可能值的三元组 #cf_span[(i,  j,  k)] 的数量。\"},{\"iden\":\"examples\",\"content\":\"输入41 1 1 1输出4输入51 3 2 3 4输出2输入61 3 3 1 3 2输出1\"},{\"iden\":\"note\",\"content\":\"在第一个例子中，Makes 总是从四个 1 中选出三个，选择它们的方式数为 #cf_span[4]。在第二个例子中，选择的三元组是数字 #cf_span[(1, 2, 3)]（指数字，而非索引）。由于有两种方式选择元素 #cf_span[3]，因此答案为 #cf_span[2]。在第三个例子中，选择的三元组是数字 #cf_span[(1, 1, 2)]，且只有一种方式选择索引。\"}]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ with $ 3 \\leq n \\leq 10^5 $.  \nLet $ A = (a_1, a_2, \\dots, a_n) $ be a sequence of positive integers with $ 1 \\leq a_i \\leq 10^9 $.\n\nLet $ T = \\{ (i,j,k) \\in \\{1,\\dots,n\\}^3 \\mid i < j < k \\} $ be the set of all valid index triples.\n\n**Constraints**  \n1. $ n \\geq 3 $  \n2. $ a_i \\geq 1 $ for all $ i \\in \\{1, \\dots, n\\} $\n\n**Objective**  \nLet $ m = \\min \\{ a_i \\cdot a_j \\cdot a_k \\mid (i,j,k) \\in T \\} $.  \nCompute the number of triples $ (i,j,k) \\in T $ such that $ a_i \\cdot a_j \\cdot a_k = m $.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF817B","tags":["combinatorics","implementation","math","sortings"],"sample_group":[["4\n1 1 1 1","4"],["5\n1 3 2 3 4","2"],["6\n1 3 3 1 3 2","1"]],"created_at":"2026-03-03 11:00:39"}}