103302: [Atcoder]ABC330 C - Minimize Abs 2

Problem Statement

You are given a positive integer $D$.

Find the minimum value of $|x^2+y^2-D|$ for non-negative integers $x$ and $y$.

Constraints

• $1\leq D \leq 2\times 10^{12}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$D$

Output

Print the answer.

Sample Input 1

21

Sample Output 1

1

For $x=4$ and $y=2$, we have $|x^2+y^2-D| = |16+4-21|=1$.

There are no non-negative integers $x$ and $y$ such that $|x^2+y^2-D|=0$, so the answer is $1$.

Sample Input 2

998244353

Sample Output 2

0

Sample Input 3

264428617

Sample Output 3

32

问题描述

给定一个正整数$D$。

求非负整数$x$和$y$的$|x^2+y^2-D|$的最小值。

限制条件

• $1\leq D \leq 2\times 10^{12}$
• 所有输入值都是整数。

输入

输入通过标准输入给出，格式如下：

$D$

输出

打印答案。

样例输入1

21

样例输出1

1

对于$x=4$和$y=2$，我们有$|x^2+y^2-D| = |16+4-21|=1$。

没有非负整数$x$和$y$使得$|x^2+y^2-D|=0$，所以答案是$1$。

样例输入2

998244353

样例输出2

0

样例输入3

264428617

样例输出3

32