{"problem":{"name":"Integer Product","description":{"content":"You are given $N$ real values $A_1, A_2, \\ldots, A_N$. Compute the number of pairs of indices $(i, j)$ such that $i < j$ and the product $A_i \\cdot A_j$ is integer.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc047_a"},"statements":[{"statement_type":"Markdown","content":"You are given $N$ real values $A_1, A_2, \\ldots, A_N$. Compute the number of pairs of indices $(i, j)$ such that $i < j$ and the product $A_i \\cdot A_j$ is integer.\n\n## Constraints\n\n*   $2 \\leq N \\leq 200\\,000$\n*   $0 < A_i < 10^4$\n*   $A_i$ is given with at most 9 digits after the decimal.\n\n## Input\n\nInput is given from Standard Input in the following format.\n\n$N$\n$A_1$\n$A_2$\n$\\vdots$\n$A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc047_a","tags":[],"sample_group":[["5\n7.5\n2.4\n17.000000001\n17\n16.000000000","3\n\nThere are 3 pairs with integer product:\n\n*   $7.5 \\cdot 2.4 = 18$\n*   $7.5 \\cdot 16 = 120$\n*   $17 \\cdot 16 = 272$"],["11\n0.9\n1\n1\n1.25\n2.30000\n5\n70\n0.000000001\n9999.999999999\n0.999999999\n1.000000001","8"]],"created_at":"2026-03-03 11:01:14"}}