Problem Description

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.

Input Format

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.

Output Format

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).

Sample Input and Output

Sample Input #1

2
A 0 0 2
B 1 0 2

Sample Output #1

5.00

Sample Input #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

Sample Output #2

205.50

见题面 Input 部分

见题面 Output 部分