A15297 | 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 $b$ ( $a<b$ ) 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.

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

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