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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.

Sample Input 1

8

Sample Output 1

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.

Sample Input 2

9

Sample Output 2

5

Sample Input 3

50

Sample Output 3

80132

Sample Input 4

10000000000

Sample Output 4

2239716

Find the count modulo $998244353$.