{"problem":{"name":"Floor, Ceil - Decomposition","description":{"content":"There is an integer $X$ written on a blackboard. You can do the operation below any number of times (possibly zero). *   Choose an integer $x$ written on the blackboard. *   Erase one $x$ from the bl","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc135_a"},"statements":[{"statement_type":"Markdown","content":"There is an integer $X$ written on a blackboard. You can do the operation below any number of times (possibly zero).\n\n*   Choose an integer $x$ written on the blackboard.\n*   Erase one $x$ from the blackboard and write two new integers $\\lfloor \\frac{x}{2}\\rfloor$ and $\\lceil \\frac{x}{2}\\rceil$.\n\nFind the maximum possible product of the integers on the blackboard after your operations, modulo $998244353$.\nWhat are $\\lfloor \\frac{x}{2}\\rfloor$ and $\\lceil \\frac{x}{2}\\rceil$?For a real number $x$, $\\lfloor x\\rfloor$ denotes the largest integer not greater than $x$, and $\\lceil x\\rceil$ denotes the smallest integer not less than $x$. For example, the following holds.\n\n*   For $x = 2$, we have $\\lfloor \\frac{x}{2}\\rfloor = 1$ and $\\lceil \\frac{x}{2}\\rceil = 1$.\n*   For $x = 3$, we have $\\lfloor \\frac{x}{2}\\rfloor = 1$, $\\lceil \\frac{x}{2}\\rceil = 2$.\n\n## Constraints\n\n*   $1\\leq X \\leq 10^{18}$\n\n## Input\n\nInput is given from Standard Input from the following format:\n\n$X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc135_a","tags":[],"sample_group":[["15","192\n\nHere is a sequence of operations that makes the product of the integers on the blackboard $192$.\n\n*   The initial state of the blackboard is $(15)$.\n*   An operation with $x = 15$ changes it to $(7, 8)$.\n*   An operation with $x = 7$ changes it to $(8, 3, 4)$.\n*   An operation with $x = 4$ changes it to $(8, 3, 2, 2)$.\n*   An operation with $x = 8$ changes it to $(3, 2, 2, 4, 4)$.\n\nHere, the product of the integers on the blackboard is $3\\times 2\\times 2\\times 4\\times 4 = 192$."],["3","3\n\nDoing zero operations makes the product of the integers on the blackboard $3$."],["100","824552442\n\nThe maximum possible product of the integers on the blackboard after your operations is $5856458868470016$, which should be printed modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}