Problem G
Toggi
Languages
en
is
Toggi loves the number $\pi $. Toggi quite likes making his computer calulate $\pi $ but that can take quite a long time, depends a bit on the number of digits he wants to calculate. If he calculates the first $n$ digits of $\pi $ it takes $n \log _{10}(n) / 10^6$ seconds, where $\log _{10}$ denotes a logarithm of base $10$. He wants to know to how many digits of $\pi $ he can calculate in the time he has. Help him find out.
Input
You are given an integer $C$, the number of seconds Toggi has.
Output
One line containing the integer $n$, the maximum number of digits of $\pi $ that Toggi can calculate in $C$ seconds.
Explanation of Sample Inputs
Toggi can calculate $189481$ digits in one second because
\[ 189481 \log _{10}(189481) / 10^6 \approx 0.9999984203540794 \leq 1 \]But he can’t calculate more digits in a single seond beause
\[ 189482 \log _{10}(189482) / 10^6 \approx 1.0000041322153754 > 1 \]Scoring
The solution will be tested on input data of varying difficulty and the data is divided into groups as shown in the table below. The solution will then be scored according to how many groups are solved.
|
Group |
Points |
Constraints |
|
1 |
10 |
$ 1 \le C \leq 5$ |
|
2 |
20 |
$ 1 \le C \leq 50$ |
|
3 |
30 |
$ 1 \le C \leq 2000$ |
|
4 |
20 |
$ 1 \le C \leq 10^4$ |
|
5 |
20 |
$ 1 \le C \leq 10^9$ |
| Sample Input 1 | Sample Output 1 |
|---|---|
1 |
189481 |
