Bob is playing with a drawing software he recently downloaded. The software loads a ~10^5~ by ~10^5~ pixel canvas for him to draw on. The pixel at ~(r, c)~ is the ~r~-th pixel from the top and the ~c~-th pixel from the left, ~1~-indexed.

Bob experimented with many tools, but he is really fascinated with the diamond coloring tool.

The diamond tool takes in a pixel location ~(x, y)~ and a weight ~w~. It then colors every pixel within a manhattan distance of ~w~ from ~(x, y)~. The manhattan distance between two pixels ~(x_1, y_1)~ and ~(x_2, y_2)~ is ~|x_1-x_2|+|y_1-y_2|~.

Bob uses the diamond tool ~N~ times. Can you determine how many pixels are colored?

Note: Python users should consider not using Python

Constraints

~1 \le N \le 100~

~1 \le x, y, w \le 10^5~

Subtask 1 [10%]

~N = 1~

~1 \le x, y, w \le 200~

Subtask 2 [20%]

~1 \le x, y, w \le 200~

Subtask 3 [30%]

~N = 1~

Subtask 4 [40%]

No additional constraints.

Input Specification

The first line of input will contain ~N~.

The next ~N~ lines will contain ~3~ space-separated integers ~x~, ~y~, and ~w~.

Output Specification

Output one integer on one line, the number of colored pixels.

Sample Input

3
2 3 3
8 4 1
4 7 2

Sample Output

38

Explanation

#####.....
##X####...
########..
.#####X##.
..#..###..
......#...
...#......
..#X#.....
...#......
..........

In the above diagram, the #'s represent colored pixels and X's represent the locations where the diamond tool was used (these are also colored).

Note that this is only a ~10~ by ~10~ snippet of the full canvas, but the rest of the canvas is empty. We can count ~38~ colored pixels.