{"problem":{"name":"J. Three Sorted Arrays","description":{"content":"This time Laltu wanted the question to be straightforward. So, given 3 1-indexed sorted arrays (A[, B[], C[])], find the number of triplets 1  ≤  i  ≤  j  ≤  k, such that: A[i]  ≤  B[j]  ≤  C[k]. Note","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":524288},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10058J"},"statements":[{"statement_type":"Markdown","content":"This time Laltu wanted the question to be straightforward. So, given 3 1-indexed sorted arrays (A[, B[], C[])], find the number of triplets 1  ≤  i  ≤  j  ≤  k, such that: A[i]  ≤  B[j]  ≤  C[k]. Note that i, j and k don’t exceed the size of respective arrays.\n\nFor example, Arrays: A  =  [1, 2, 3, 4] B  =  [5, 6, 7, 8] C  =  [9, 10, 11, 12]\n\nThe triplet (i, j, k)  =  (1, 2, 3) has to be considered because: A[1]  ≤  B[2]  ≤  C[3].\n\nFirst line contains T, the number of test cases. Each test case consists of: P, the length of first array. The next line will consist of P integers. Q, the length of second array. The next line will consist of Q integers. R, the length of third array. The next line will consist of R integers.\n\nFor each test case print the required answer in one line.\n\n*Constraints* \n\nThe possible triplets (i, j, k) are: (1, 1, 1) (1, 1, 2) (1, 1, 3) (1, 2, 2) (1, 2, 3) (1, 3, 3)\n\n## Input\n\nFirst line contains T, the number of test cases. Each test case consists of: P, the length of first array. The next line will consist of P integers. Q, the length of second array. The next line will consist of Q integers. R, the length of third array. The next line will consist of R integers.\n\n## Output\n\nFor each test case print the required answer in one line.*Constraints*   1  ≤  T  ≤  3  1  ≤  P, Q, R  ≤  105   - 109  ≤  Elements of arrays  ≤  109 \n\n[samples]\n\n## Note\n\nThe possible triplets (i, j, k) are: (1, 1, 1) (1, 1, 2) (1, 1, 3) (1, 2, 2) (1, 2, 3) (1, 3, 3)","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case:  \n- Let $ P, Q, R \\in \\mathbb{Z}^+ $ denote the lengths of arrays $ A $, $ B $, and $ C $, respectively.  \n- Let $ A = (a_1, a_2, \\dots, a_P) $, $ B = (b_1, b_2, \\dots, b_Q) $, $ C = (c_1, c_2, \\dots, c_R) $ be three 1-indexed sorted arrays of integers.\n\n**Constraints**  \n1. $ T \\geq 1 $  \n2. For each test case:  \n   - $ 1 \\leq P, Q, R \\leq \\text{some upper bound (implied by context)} $  \n   - $ a_1 \\leq a_2 \\leq \\dots \\leq a_P $  \n   - $ b_1 \\leq b_2 \\leq \\dots \\leq b_Q $  \n   - $ c_1 \\leq c_2 \\leq \\dots \\leq c_R $  \n\n**Objective**  \nCount the number of triplets $ (i, j, k) \\in \\{1, \\dots, P\\} \\times \\{1, \\dots, Q\\} \\times \\{1, \\dots, R\\} $ such that:  \n$$\na_i \\leq b_j \\leq c_k\n$$","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10058J","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}