CF1032D.Barcelonian Distance

In this problem we consider a very simplified model of Barcelona city.

Barcelona can be represented as a plane with streets of kind $x = c$ and $y = c$ for every integer $c$ (that is, the rectangular grid). However, there is a detail which makes Barcelona different from Manhattan. There is an avenue called Avinguda Diagonal which can be represented as a the set of points $(x, y)$ for which $ax + by + c = 0$.

One can walk along streets, including the avenue. You are given two integer points $A$ and $B$ somewhere in Barcelona. Find the minimal possible distance one needs to travel to get to $B$ from $A$.

本题中，我们考虑一个高度简化的巴塞罗那城市模型。

巴塞罗那可被表示为一个平面，其街道由所有形如 $x = c$ 和 $y = c$ 的直线构成（其中 $c$ 为任意整数），即一个矩形网格。然而，有一个细节使巴塞罗那区别于曼哈顿：存在一条名为“对角大道”（Avinguda Diagonal）的主干道，它可被表示为满足方程 $ax + by + c = 0$ 的所有点 $(x, y)$ 构成的集合。

人们可以沿街道（包括该大道）行走。现给定巴塞罗那中的两个整数坐标点 $A$ 和 $B$。求从 $A$ 出发到达 $B$ 所需的最短路径长度。

The first line contains three integers $a$, $b$ and $c$ ($-10^9\leq a, b, c\leq 10^9$, at least one of $a$ and $b$ is not zero) representing the Diagonal Avenue.

The next line contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-10^9\leq x_1, y_1, x_2, y_2\leq 10^9$) denoting the points $A = (x_1, y_1)$ and $B = (x_2, y_2)$.

第一行包含三个整数 $a$、$b$ 和 $c$（$-10^9\leq a, b, c\leq 10^9$，且 $a$ 与 $b$ 中至少有一个不为零），表示对角线大道。

下一行包含四个整数 $x_1$、$y_1$、$x_2$ 和 $y_2$（$-10^9\leq x_1, y_1, x_2, y_2\leq 10^9$），表示点 $A = (x_1, y_1)$ 和 $B = (x_2, y_2)$。

Find the minimum possible travel distance between $A$ and $B$. Your answer is considered correct if its absolute or relative error does not exceed $10^{-6}$.

Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is accepted if and only if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$.

求 $A$ 与 $B$ 之间可能的最小旅行距离。若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

形式化地，设你的答案为 $a$，评测组的答案为 $b$。当且仅当 $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$ 时，你的答案被接受。

The first example is shown on the left picture while the second example us shown on the right picture below. The avenue is shown with blue, the origin is shown with the black dot.

第一个示例显示在左侧图中，第二个示例显示在下方右侧图中。大道用蓝色表示，原点用黑点表示。