[email protected] #6 Math

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Hsara and Simone like to communicate without anyone else knowing what they’re saying. This time, Simone invented a very sneaky cipher. When she wants to tell Hsara a non-negative number $n$, she performs the following encryption procedure.

Let $d(n)$ denote the decimal expansion of $n$. Consider the string $x := d(n)^ n$, i.e., the decimal expansion of $n$ concatenated with itself $n$ times. The encryption of $n$ is then the length of $x$.

As an example, assume Simone wants to encrypt the number $10$. Then

\[ x = 10101010101010101010. \]The length of $x$ is then $20$, which will be the encrypted value of $x$.

Hsara had no problem writing a decryption algorithm for this procedure. But can you?

The first and only line contains an integer $L$ ($0 \leq L \leq 10^{{10}^6}$), the encrypted value of some non-negative integer $n$.

Output a single line containing the integer $n$.

Sample Input 1 | Sample Output 1 |
---|---|

20 |
10 |