103543: [Atcoder]ABC354 D - AtCoder Wallpaper

Problem Statement

The pattern of AtCoder's wallpaper can be represented on the $xy$-plane as follows:

• The plane is divided by the following three types of lines:
  • $x = n$ (where $n$ is an integer)
  • $y = n$ (where $n$ is an even number)
  • $x + y = n$ (where $n$ is an even number)
• Each region is painted black or white. Any two regions adjacent along one of these lines are painted in different colors.
• The region containing $(0.5, 0.5)$ is painted black.

The following figure shows a part of the pattern.

You are given integers $A, B, C, D$. Consider a rectangle whose sides are parallel to the $x$- and $y$-axes, with its bottom-left vertex at $(A, B)$ and its top-right vertex at $(C, D)$. Calculate the area of the regions painted black inside this rectangle, and print twice that area.

It can be proved that the output value will be an integer.

Constraints

• $-10^9 \leq A, B, C, D \leq 10^9$
• $A < C$ and $B < D$.
• All input values are integers.

Input

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

$A$ $B$ $C$ $D$

Output

Print the answer on a single line.

Sample Input 1

0 0 3 3

Sample Output 1

10

We are to find the area of the black-painted region inside the following square:

The area is $5$, so print twice that value: $10$.

Sample Input 2

-1 -2 1 3

Sample Output 2

11

The area is $5.5$, which is not an integer, but the output value is an integer.

Sample Input 3

-1000000000 -1000000000 1000000000 1000000000

Sample Output 3

4000000000000000000

This is the case with the largest rectangle, where the output still fits into a 64-bit signed integer.

问题描述

AtCoder的壁纸图案在笛卡尔坐标系$xy$平面上可以表示如下：

• 平面被以下三种类型的线分成多个区域：
  • $x = n$（其中$n$是整数）
  • $y = n$（其中$n$是偶数）
  • $x + y = n$（其中$n$是偶数）
• 每个区域被涂成黑色或白色。沿着这些线相邻的两个区域颜色不同。
• 包含点$(0.5, 0.5)$的区域被涂成黑色。

以下图显示了图案的一部分。

给你四个整数$A, B, C, D$。考虑一个长和宽平行于$x$轴和$y$轴的矩形，其左下角坐标为$(A, B)$，右上角坐标为$(C, D)$。计算这个矩形内部被涂成黑色的区域的面积，并输出该面积的两倍。

可以证明输出的值是一个整数。

约束

• $-10^9 \leq A, B, C, D \leq 10^9$
• $A < C$ 且 $B < D$。
• 所有输入值都是整数。

输入

标准输入提供以下格式的输入：

$A$ $B$ $C$ $D$

输出

在一行中打印答案。

样例输入1

0 0 3 3

样例输出1

10

我们需要找到以下正方形内黑色区域的面积：

面积为$5$，所以输出其两倍值：$10$。

样例输入2

-1 -2 1 3

样例输出2

11

面积为$5.5$，不是一个整数，但输出值是一个整数。

样例输入3

-1000000000 -1000000000 1000000000 1000000000

样例输出3

4000000000000000000

这是最大的矩形情况，输出仍然能容纳在一个64位有符号整数内。