1725G · Garage

Problem: 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 $b$ ($a<b$) 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.

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

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

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