# #JC0106. Reachable Numbers

# Reachable Numbers

## Description

Let's denote a function $f(x)$ in such a way: we add $1$ to $x$, then, while there is at least one trailing zero in the resulting number, we remove that zero. For example,

- $f(599) = 6$: $599 + 1 = 600 \rightarrow 60 \rightarrow 6$;
- $f(7) = 8$: $7 + 1 = 8$;
- $f(9) = 1$: $9 + 1 = 10 \rightarrow 1$;
- $f(10099) = 101$: $10099 + 1 = 10100 \rightarrow 1010 \rightarrow 101$.

We say that some number $y$ is reachable from $x$ if we can apply function $f$ to $x$ some (possibly zero) times so that we get $y$ as a result. For example, $102$ is reachable from $10098$ because $f(f(f(10098))) = f(f(10099)) = f(101) = 102$; and any number is reachable from itself.

You are given a number $n$; your task is to count how many different numbers are reachable from $n$.

## Input

The first line contains one integer $n$ ($1 \le n \le 10^9$).

## Output

Print one integer: the number of different numbers that are reachable from $n$.

```
1098
```

```
20
```

```
10
```

```
19
```

## Note

The numbers that are reachable from $1098$ are:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1098, 1099$.