Score : $500$ points

Problem Statement

You have an integer $1$ and a die that shows integers between $1$ and $6$ (inclusive) with equal probability. You repeat the following operation while your integer is strictly less than $N$:

• Cast a die. If it shows $x$, multiply your integer by $x$.

Find the probability, modulo $998244353$, that your integer ends up being $N$.

Constraints

• $2 \leq N \leq 10^{18}$
• $N$ is an integer.

Input

The input is given from Standard Input in the following format:

$N$

Output

Print the probability, modulo $998244353$, that your integer ends up being $N$.

6

239578645

One of the possible procedures is as follows.

• Initially, your integer is $1$.
• You cast a die, and it shows $2$. Your integer becomes $1 \times 2 = 2$.
• You cast a die, and it shows $4$. Your integer becomes $2 \times 4 = 8$.
• Now your integer is not less than $6$, so you terminate the procedure.

Your integer ends up being $8$, which is not equal to $N = 6$.

The probability that your integer ends up being $6$ is $\frac{7}{25}$. Since $239578645 \times 25 \equiv 7 \pmod{998244353}$, print $239578645$.

7

0

No matter what the die shows, your integer never ends up being $7$.

300

183676961

979552051200000000

812376310