Escalator

Interview

Time limit1sMemory limit512 MB

Summary

Given n, sum the decimal digit counts of the numbers 1, n, and every multiple of 10 up to n.

Level: Medium4 of 10
Topics: Math, Implementation, Number theory
Solved: No attempts yet

Problem

A new metro station is opening in Saint Petersburg, and an escalator must be produced for it. The escalator consists of $n$ steps, numbered with the integers from $1$ to $n$ . By tradition, the step numbers are written on the steps whose numbers are multiples of ten, as well as on the first and the last step. Writing a number uses the same amount of paint for each digit written.

To calculate the amount of paint needed, you have to know how many digits will be written. Write a program that determines the total number of digits used in the numbers of the labeled steps.

Input

The input file contains a single integer $n$ , the number of steps of the escalator ( $1 \le n \le 10^{12}$ ).

Output

Output the total number of digits in the numbers of the labeled steps.

Hint

In the first example, numbers are written on steps 1, 10, 20; in the second, on 1, 10, 20, 23.

Examples2

Example 1
Input
```
20
```
Expected output
```
5
```
Example 2
Input
```
23
```
Expected output
```
7
```