{"problem":{"name":"Happy New Year 2023","description":{"content":"You are given a positive integer $N$. It is known that $N$ can be represented as $N=p^2q$ using two different prime numbers $p$ and $q$. Find $p$ and $q$. You have $T$ test cases to solve.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc284_d"},"statements":[{"statement_type":"Markdown","content":"You are given a positive integer $N$. It is known that $N$ can be represented as $N=p^2q$ using two different prime numbers $p$ and $q$.\nFind $p$ and $q$.\nYou have $T$ test cases to solve.\n\n## Constraints\n\n*   All values in the input are integers.\n*   $1\\leq T\\leq 10$\n*   $1\\leq N \\leq 9\\times 10^{18}$\n*   $N$ can be represented as $N=p^2q$ using two different prime numbers $p$ and $q$.\n\n## Input\n\nThe input is given from Standard Input in the following format, where $\\text{test}_i$ represents the $i$\\-th test case:\n\n$T$\n$\\text{test}_1$\n$\\text{test}_2$\n$\\vdots$\n$\\text{test}_T$\n\nEach test case is in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc284_d","tags":[],"sample_group":[["3\n2023\n63\n1059872604593911","17 7\n3 7\n104149 97711\n\nFor the first test case, we have $N=2023=17^2\\times 7$. Thus, $p=17$ and $q=7$."]],"created_at":"2026-03-03 11:01:13"}}