Score : $400$ points

问题描述

给定一个大于等于2的整数 $K$。

求最小的正整数 $N$，使得 $N!$ 是 $K$ 的倍数。

此处，$N!$ 表示 $N$ 的阶乘。在本问题的约束条件下，可以证明这样的 $N$ 总是存在。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an integer $K$ greater than or equal to $2$.
Find the minimum positive integer $N$ such that $N!$ is a multiple of $K$.

Here, $N!$ denotes the factorial of $N$. Under the Constraints of this problem, we can prove that such an $N$ always exists.

Constraints

• $2\leq K\leq 10^{12}$
• $K$ is an integer.

Input

The input is given from Standard Input in the following format:

$K$

Output

Print the minimum positive integer $N$ such that $N!$ is a multiple of $K$.

Sample Input 1

30

Sample Output 1

5

• $1!=1$
• $2!=2\times 1=2$
• $3!=3\times 2\times 1=6$
• $4!=4\times 3\times 2\times 1=24$
• $5!=5\times 4\times 3\times 2\times 1=120$

Therefore, $5$ is the minimum positive integer $N$ such that $N!$ is a multiple of $30$. Thus, $5$ should be printed.

Sample Input 2

123456789011

Sample Output 2

123456789011

Sample Input 3

280

Sample Output 3

7

update @ 2024/3/10 11:46:11