{"raw_statement":[{"iden":"problem statement","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 $\\lfloor \\frac{x}{2}\\rfloor = 1$, $\\lceil \\frac{x}{2}\\rceil = 2$."},{"iden":"constraints","content":"*   $1\\leq X \\leq 10^{18}$"},{"iden":"input","content":"Input is given from Standard Input from the following format:\n\n$X$"},{"iden":"sample input 1","content":"15"},{"iden":"sample output 1","content":"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 $3\\times 2\\times 2\\times 4\\times 4 = 192$."},{"iden":"sample input 2","content":"3"},{"iden":"sample output 2","content":"3\n\nDoing zero operations makes the product of the integers on the blackboard $3$."},{"iden":"sample input 3","content":"100"},{"iden":"sample output 3","content":"824552442\n\nThe maximum possible product of the integers on the blackboard after your operations is $5856458868470016$, which should be printed modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}