Given n disks, find the total number of lattice points covered by these disks.

Input: First line has a single input n. Next n lines have three space separated integers ai, bi, ri for a disk with center (ai, bi) and radius ri.

Output: Print a number z which corresponds to, the number of lattice points covered by the disks.

Constraints: 0 => 0 => n=>

Constraints for 30% of total score: 0=> n=>

Note: Lattice points are points with integer coordinates. A point is covered by a disk if it lies either on the boundary or inside the disk.

Sample: Input: 2 3 3 2 2 2 1 Output: 15

(See this diagram for how the dots are counted:)

in python