CF991F.Concise and clear

Vasya is a regular participant at programming contests and is already experienced in finding important sentences in long statements. Of course, numbers constraints are important — factorization of a number less than 1000000 is easier than of a number less than 1000000000. However, sometimes it's hard to understand the number at the first glance. Could it be shortened? For example, instead of 1000000 you could write $10^{6}$, instead of 1000000000 —$10^{9}$, instead of 1000000007 — $10^{9}+7$.

Vasya decided that, to be concise, the notation should follow several rules:

• the notation should only consist of numbers, operations of addition ("+"), multiplication ("*") and exponentiation ("^"), in particular, the use of braces is forbidden;
• the use of several exponentiation operations in a row is forbidden, for example, writing "2³4" is unacceptable;
• the value of the resulting expression equals to the initial number;
• the notation should consist of the minimal amount of symbols.

Given $n$, find the equivalent concise notation for it.

瓦西里是编程竞赛的常客，早已熟练于在冗长的题目描述中找出关键句。当然，数据范围很重要——分解一个小于 $1000000$ 的数，比分解一个小于 $1000000000$ 的数要容易得多。然而，有时仅凭第一眼很难理解某个数字的量级。能否将其简写呢？例如，用 $10^{6}$ 代替 $1000000$，用 $10^{9}$ 代替 $1000000000$，用 $10^{9}+7$ 代替 $1000000007$。

瓦西里决定，为保证简洁性，该简写记法需满足以下规则：

• 记法中仅可包含数字、加法（“+”）、乘法（“*”）和幂运算（“^”）运算符；特别地，不允许使用括号；
• 不允许连续使用多个幂运算符，例如，“2³4” 是不合法的；
• 该表达式的计算结果必须严格等于原数；
• 该表达式所含字符总数应为最小可能值。

给定正整数 $n$，请找出其满足上述条件的最短等价简写表达式。

The only line contains a single integer $n$ ($1 \leq n \leq 10\,000\,000\,000$).

唯一的一行包含一个整数 $n$（$1 \leq n \leq 10\,000\,000\,000$）。

Output a concise notation of the number $n$. If there are several concise notations, output any of them.

输出数字 $n$ 的简洁表示法。如果存在多种简洁表示法，则输出其中任意一种。

The third sample allows the answer 10^10 also of the length $5$.

第三个样例允许答案 $10^10$，其长度也为 $5$。