CF986D.Perfect Encoding

You are working as an analyst in a company working on a new system for big data storage. This system will store $n$ different objects. Each object should have a unique ID.

To create the system, you choose the parameters of the system — integers $m \ge 1$ and $b_{1}, b_{2}, \ldots, b_{m}$. With these parameters an ID of some object in the system is an array of integers $[a_{1}, a_{2}, \ldots, a_{m}]$ where $1 \le a_{i} \le b_{i}$ holds for every $1 \le i \le m$.

Developers say that production costs are proportional to $\sum_{i=1}^{m} b_{i}$. You are asked to choose parameters $m$ and $b_{i}$ so that the system will be able to assign unique IDs to $n$ different objects and production costs are minimized. Note that you don't have to use all available IDs.

你是一家致力于开发新型大数据存储系统公司的分析师。该系统将存储 $n$ 个不同的对象，每个对象必须具有唯一的 ID。

为构建该系统，你需要选定系统参数——整数 $m \ge 1$ 和 $b_{1}, b_{2}, \ldots, b_{m}$。在这些参数下，系统中某个对象的 ID 是一个整数数组 $[a_{1}, a_{2}, \ldots, a_{m}]$，其中对每个 $1 \le i \le m$ 均满足 $1 \le a_{i} \le b_{i}$。

开发人员指出，生产成本与 $\sum_{i=1}^{m} b_{i}$ 成正比。你的任务是选择参数 $m$ 和 $b_{i}$，使得系统能够为 $n$ 个不同对象分配唯一的 ID，同时使生产成本最小化。注意：你无需用尽所有可能的 ID。

In the only line of input there is one positive integer $n$. The length of the decimal representation of $n$ is no greater than $1.5 \cdot 10^{6}$. The integer does not contain leading zeros.

输入仅有一行，包含一个正整数 $n$。$n$ 的十进制表示的长度不超过 $1.5 \cdot 10^{6}$。该整数不含前导零。

Print one number — minimal value of $\sum_{i=1}^{m} b_{i}$.

输出一个数字——$\sum_{i=1}^{m} b_{i}$ 的最小值。