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 $N$.

How to find a probability modulo $998244353$? We can prove that the sought probability is always rational. Additionally, under the constraints of this problem, when that value is represented as $\\frac{P}{Q}$ with two coprime integers $P$ and $Q$, we can prove that there is a unique integer $R$ such that $R \\times Q \\equiv P\\pmod{998244353}$ and $0 \\leq R \\lt 998244353$. Find this $R$.

Constraints

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

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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 $N$.

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Sample Input 1

6

Sample Output 1

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 $239578645$.

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Sample Input 2

7

Sample Output 2

0

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

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Sample Input 3

300

Sample Output 3

183676961

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Sample Input 4

979552051200000000

Sample Output 4

812376310