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).

2
A 0 0 2
B 1 0 2

5.00

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

205.50