Garage

题意翻译

给出$N$，请求出$b^2 - a ^ 2$的第$N$小值，其中$a, b \in \mathbb{N}^+$

题目描述

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.

输入输出格式

输入格式

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

输出格式

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

输入输出样例

输入样例 #1

3

输出样例 #1

7

说明

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