201270: [AtCoder]ARC127 A - Leading 1s

Problem Statement

For an integer $x$, let $f(x)$ be the number of leading ones in the decimal notation of $x$. For example, we have $f(1)=1,f(2)=0,f(10)=1,f(11)=2,f(101)=1$.

Given an integer $N$, find $f(1)+f(2)+\cdots+f(N)$.

Constraints

• $1 \leq N \leq 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

Sample Input 1

11

Sample Output 1

4

We have $f(2)=f(3)=\cdots =f(9)=0$. The answer is $f(1)+f(10)+f(11)=4$.

Sample Input 2

120

Sample Output 2

44

Sample Input 3

987654321

Sample Output 3

123456789