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 < ai, bi <= 500
0 < ri <= min(ai, bi, 500)
n<= 500

Constraints for 30% of total score:
0< ai, bi <= 10
n<= 5

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:)