#AT1774. F - Cube

F - Cube

F - Cube

Score : $600$ points

Problem Statement

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 they only differ by rotation. (Numbers have no direction.)

The count can be enormous, so find it modulo $998244353$.

Constraints

  • $6 \leq S \leq 10^{18}$
  • $S$ is an integer.

Input

Input is given from Standard Input in the following format:

SS

Output

Print the count modulo $998244353$.


8
3

We 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

Find the count modulo $998244353$.