{"problem":{"name":"Cube","description":{"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 $S$? Here, two ways to write numbers are not distinguished when","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc198_f"},"statements":[{"statement_type":"Markdown","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 $998244353$.\n\n## Constraints\n\n*   $6 \\leq S \\leq 10^{18}$\n*   $S$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$S$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc198_f","tags":[],"sample_group":[["8","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."],["9","5"],["50","80132"],["10000000000","2239716\n\nFind the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:13"}}