Factorial

You have probably seen the following problem before.

Items (2) and (3) are easy, so we focus especially on (1).

At first glance it seems that summing logarithms carefully will do the job, but if you simply write the code that way, floating-point error is a concern.

Kipa is setting this problem, and intends to include as test cases the situations where floating-point error is likely to occur when solving (1).

Help Kipa.

There is no input.

Output one positive integer. The integer you output must be at least 7 and at most 100000000000000.

(The source states no constraints.)

Let the number you output be $N$, and define the following real number $x_{N}$.

$x_{N} := N! \cdot 10^{1 - \left\lfloor \log_{10}(N!) \right\rfloor}$

For the value $\varepsilon = 1.5 \times 10^{-14}$ fixed in advance by the judges, the real number $S$ related to your score is as follows.

$S = 998244353 \cdot \min\left\{1, \frac{\varepsilon}{\left|x_{N} - \left\lfloor x_{N} + 0.5 \right\rfloor \right|}\right\}$

If $S = 998244353$, you receive 998244353 points. Otherwise, the difference between your score and $S$ is guaranteed to be at most $0.02$.

Your score is always an integer multiple of $0.01$.