{"raw_statement":[{"iden":"problem statement","content":"Let us write a positive integer on each face of a cube. How many ways are there to do this so that the sum of the six numbers written is $S$?\nHere, two ways to write numbers are not distinguished when they only differ by rotation. (Numbers have no direction.)\nThe count can be enormous, so find it modulo $998244353$."},{"iden":"constraints","content":"*   $6 \\leq S \\leq 10^{18}$\n*   $S$ is an integer."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$S$"},{"iden":"sample input 1","content":"8"},{"iden":"sample output 1","content":"3\n\nWe have one way to write $1,1,1,1,1,3$ on the cube and two ways to write $1,1,1,1,2,2$ (one where we write $2$ on adjacent faces and another where we write $2$ on opposite faces), for a total of three ways."},{"iden":"sample input 2","content":"9"},{"iden":"sample output 2","content":"5"},{"iden":"sample input 3","content":"50"},{"iden":"sample output 3","content":"80132"},{"iden":"sample input 4","content":"10000000000"},{"iden":"sample output 4","content":"2239716\n\nFind the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}