AlanL's friends are busy orzing him as AlanL is very orz. AlanL has ~N~ friends situated on the 2D plane, where each of his friends are located on a lattice point (point with integer-valued coordinates). Each of AlanL's friends is able to orz AlanL if he is on or inside a circle of radius ~R_i~. Can you count how many lattice points AlanL can be on such that is he orz'd by at least one of his friends?

Input Specification

The first line will contain ~N\ (1 \le N \le 2 \times 10^3)~.

The next ~N~ lines will contain 3 integers ~x_i, y_i, R_i\ (0 \le x_i, y_i, \le 10^9),\ (1 \le R_i \le 2 \times 10^3)~, the coordinates and radius of AlanL's ~i^{th}~ friend.

Output Specification

Output the number of lattice points on one line.

Subtasks

Subtask 1 [20%]

~(0 \le N, x_i, y_i, R_i \le 100)~

~(x_i, y_i \ge R_i)~

Subtask 2 [30%]

~(0 \le x_i, y_i \le 10^4)~

Subtask 3 [50%]

No further constraints.

Sample Input

2
1 1 1
2 1 1

Sample Output

8