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.

Input

Input is given from Standard Input in the following format:
S

Output

Print the count 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.

见题面 Input 部分

见题面 Output 部分