CF1157A.Reachable Numbers

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 $n$.

我们定义一个函数 $f(x)$ 如下：先将 $x$ 加 $1$，然后，只要所得数字末尾至少有一个 $0$，就将其末尾的 $0$ 去掉。例如：

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

若对 $x$ 重复（可能零次）应用函数 $f$ 可得到 $y$，则称数 $y$ 是从 $x$ 可达的。例如，$102$ 是从 $10098$ 可达的，因为 $f(f(f(10098))) = f(f(10099)) = f(101) = 102$；且任意数均从自身可达。

给定一个数 $n$，你的任务是计算从 $n$ 出发可达的不同数字的个数。

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

第一行包含一个整数 $n$（$1 \le n \le 10^9$）。

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

输出一个整数：从 $n$ 出发可达的不同数字的个数。

The numbers that are reachable from $1098$ are:

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

从 $1098$ 可达的数有：

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