CF1242A.Tile Painting

Ujan has been lazy lately, but now has decided to bring his yard to good shape. First, he decided to paint the path from his house to the gate.

The path consists of $n$ consecutive tiles, numbered from $1$ to $n$. Ujan will paint each tile in some color. He will consider the path aesthetic if for any two different tiles with numbers $i$ and $j$, such that $|j - i|$ is a divisor of $n$ greater than $1$, they have the same color. Formally, the colors of two tiles with numbers $i$ and $j$ should be the same if $|i-j| \gt 1$ and $n \bmod |i-j| = 0$ (where $x \bmod y$ is the remainder when dividing $x$ by $y$).

Ujan wants to brighten up space. What is the maximum number of different colors that Ujan can use, so that the path is aesthetic?

乌詹最近一直很懒，但现在他决定把自家院子好好收拾一番。首先，他决定粉刷从房子到大门的小路。

这条小路由 $n$ 块连续的瓷砖组成，编号从 $1$ 到 $n$。乌詹将为每块瓷砖涂上某种颜色。当且仅当对任意两个编号分别为 $i$ 和 $j$ 的不同瓷砖，若 $|j - i|$ 是 $n$ 的一个大于 $1$ 的约数，则它们的颜色必须相同，此时该路径才被视为“美观”。形式化地说：若 $|i-j| \gt 1$ 且 $n \bmod |i-j| = 0$（其中 $x \bmod y$ 表示 $x$ 除以 $y$ 的余数），则编号为 $i$ 和 $j$ 的两块瓷砖的颜色必须相同。

乌詹希望让空间更明亮多彩。那么，在保证路径美观的前提下，乌詹最多能使用多少种不同的颜色？

The first line of input contains a single integer $n$ ($1 \leq n \leq 10^{12}$), the length of the path.

输入的第一行包含一个整数 $n$（$1 \leq n \leq 10^{12}$），表示路径的长度。

Output a single integer, the maximum possible number of colors that the path can be painted in.

输出一个整数，表示该路径最多可以被涂成的颜色种数。

In the first sample, two colors is the maximum number. Tiles $1$ and $3$ should have the same color since $4 \bmod |3-1| = 0$. Also, tiles $2$ and $4$ should have the same color since $4 \bmod |4-2| = 0$.

In the second sample, all five colors can be used.

在第一个样例中，最多可以使用两种颜色。由于 $4 \bmod |3-1| = 0$，因此第 $1$ 块与第 $3$ 块瓷砖必须涂成同一种颜色；又因 $4 \bmod |4-2| = 0$，所以第 $2$ 块与第 $4$ 块瓷砖也必须涂成同一种颜色。

在第二个样例中，全部五种颜色均可使用。