CF1725G.Garage

Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.

Define $a$ and $b$ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer $x$ is suitable if and only if we can construct a garage with assigning positive integer values for the lengths $a$ and $b$ ($a \lt b$) so that the area of the square at the bottom is exactly $x$. As a good friend of Pak Chanek, you are asked to help him find the $N$-th smallest suitable number.

Pak Chanek 计划建造一个车库。他希望该车库由一个正方形和一个直角三角形组成，其布局如下图所示。

如图所示，定义 $a$ 和 $b$ 为直角三角形的两条边的长度。当且仅当存在正整数 $a$ 和 $b$（满足 $a < b$），使得底部正方形的面积恰好为 $x$ 时，称整数 $x$ 是“合适的”。作为 Pak Chanek 的好朋友，你需要帮助他找出第 $N$ 个最小的合适数。

The only line contains a single integer $N$ ($1 \leq N \leq 10^9$).

唯一的一行包含一个整数 $N$（$1 \leq N \leq 10^9$）。

An integer that represents the $N$-th smallest suitable number.

表示第 $N$ 个最小的合适数的一个整数。

The $3$-rd smallest suitable number is $7$. A square area of $7$ can be obtained by assigning $a=3$ and $b=4$.

第 $3$ 个合适的数是 $7$。通过令 $a=3$ 且 $b=4$，可得到面积为 $7$ 的正方形。