# [CERC2017]Lunar Landscape

## 题意翻译

（具体字母格式懒得操作） 月球的景观 题目描述 一个卫星正在为探测车在月球上寻找一个合适的降落区。降落区被看做在平面直角坐标系中的一个方形区域。 这颗卫星已经照了n张照片，每张照片都涵盖了月球表面的一块正方形区域。经过对相机的精细校准，可以保证所有照片涵盖的区域都和坐标对齐——正方形四个角的坐标都为整数。由于卫星的轨道一直在变化，所以照片有两种形式： ·A类照片的边缘和坐标轴平行。对于这样的照片，题目将会给出它中心的坐标(x,y)和它的边长a（a为偶数）。 ·B类照片的边缘和坐标轴呈45°角。对于这样的照片，题目将会给出它中心的坐标(x,y)和它对角线的长度d（d为偶数）。 求出卫星图片拍摄到平面的总大小。 输入输出格式 输入格式： 第一行有一个整数n(1≤n≤200000)表示照片的数量。接下来n行中第j行的格式是"A xj yj aj"或"B xj yj dj" ，分别表示这张照片的类型是A或B。 xj和yj是这张图片中心的坐标(1000≤xj,yj≤1000)。aj和dj为偶数(2≤aj,dj≤1000)，分别表示正方形的边长和对角线长度。 输出格式： 输出平面总的大小，保留两位小数。答案必须和标准答案严格相等（精度问题零容忍↖(^ω^)↗）。

## 题目描述

A satellite is surveying a possible rover landing area on the moon. The landing area is modeled as a square grid embedded in the standard coordinate system. The satellite has taken \$n\$ photos, each capturing a square area of the surface. Careful camera calibration has ensured that all photos are aligned with the grid — all four vertices have integer coordinates. Due to the satellite’s changing orbit there are two types of photos: - Photos of type ``A`` have sides that are parallel to coordinate axes. Such a photo is specified by giving the integer coordinates \$(x, y)\$ of the square’s middle point and the length of its side \$a\$ — always an even integer. - Photos of type ``B`` have sides at a \$45^{\circ}\$ angle to the coordinate axes. Such a photo is specified by giving the integer coordinates \$(x, y)\$ of the square’s middle point and the length of its diagonal \$d\$ — always an even integer. Find the total surface area captured in the satellite photos.

## 输入输出格式

### 输入格式

The first line contains an integer \$n(1 \le n \le 200 000)\$ — the number of photos. The \$j-th\$ of the following \$n\$ lines is either of the form “\$A \ x_j \ y_j \ a_j\$” or “\$B \ x_j \ y_j \ d_j\$” representing a photo of type ``A`` or ``B``,respectively. The \$x_j\$ and \$y_j\$ are the integer coordinates of the middle point of the photo \$(-1 000 \le x_j, y_j \le 1 000)\$. The \$a_j\$ and \$d_j\$ are even integers \$(2 \le a_j, d_j \le 1 000)\$ — the side length and the diagonal length, respectively.

### 输出格式

Output a number with exactly two digits after the decimal point — the total area of the surface. The answer has to exactly correspond to the judge’s solution (no rounding errors are tolerated).

## 输入输出样例

### 输入样例 #1

``````2
A 0 0 2
B 1 0 2``````

### 输出样例 #1

``5.00``

### 输入样例 #2

``````8
A -7 10 4
B 3 10 8
A -6 6 6
A -2 5 8
B 3 -1 8
B -7 -4 8
A 3 9 2
B 8 6 6
``````

### 输出样例 #2

``205.50``