Pixel Triangles

A 2000×2000 grid is given, and each pixel (cell) is identified by its row and column. The leftmost column is column 1, and the topmost row is row 1.

A pixel triangle is defined as follows.

• The pixel in row x, column y is written as (x, y), and a pixel triangle consists of several pixels.
• A pixel triangle is written as $P(A, B, C)$ for three positive integers A, B, and C.
• $P(A, B, C) = \{ (x, y) \mid A \le x,\ B \le y,\ 0 \le (x-A) + (y-B) \le C-1 \}$
• Every pixel making up a pixel triangle on the grid is guaranteed to lie inside the grid.

Given n pixel triangles made of grid pixels, print the number of pixels the triangles cover.

Different pixel triangles may share the same pixel.

For example, when n = 3 and the three given pixel triangles are $P(1, 2, 3), P(3, 1, 2), P(5, 5, 1)$, the state of the grid is depicted below.

Figure: A portion of the grid

The number of pixels covered in the end is 9.

The first line gives the number of pixel triangles n. Each of the following n lines gives three integers A, B, C describing one pixel triangle.

Print the number of covered pixels.

• 1 ≤ n ≤ 4,000,000
• 1 ≤ A, B, C ≤ 2,000
• 1 ≤ A + C - 1, B + C - 1 ≤ 2,000