Lunar Landscape

문제

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 Ahave 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 Bhave sides at a 45^◦ 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.

입력

The first line contains an integer n (1 ≤ n ≤ 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 ≤ x_j, y_j ≤ 1 000). The a_j and d_j are even integers (2 ≤ a_j, d_j ≤ 1 000) — the side length and the diagonal length, respectively

출력

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).

힌트

Sample 1: 

Sample 2: 

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