Cow-libi

문제

Somebody has been grazing in Farmer John's $(1\le G\le {10}^5)(1\; \backslash le\; G\; \backslash le\; 10^5)$ private gardens! Using his expert forensic knowledge, FJ has been able to determine the precise time each garden was grazed. He has also determined that there was a single cow that was responsible for every grazing incident.

In response to these crimes each of FJ's $NN$ $(1\le N\le {10}^5)(1\; \backslash le\; N\; \backslash le\; 10^5)$ cows have provided an alibi that proves the cow was in a specific location at a specific time. Help FJ test whether each of these alibis demonstrates the cow's innocence.

A cow can be determined to be innocent if it is impossible for her to have travelled between all of the grazings and her alibi. Cows travel at a rate of 1 unit distance per unit time.

입력

The first line of input will contain $GG$ and $NN$ separated by a space.

The next $GG$ lines contain the integers $xx$, $yy$, and $tt$ $(-{10}^9\le x,y\le {10}^9;0\le t\le {10}^9)(-10^9\; \backslash le\; x,\; y\; \backslash le\; 10^9;\; 0\; \backslash le\; t\; \backslash le\; 10^9)$ separated by a space describing the location and time of the grazing. It will always be possible for a single cow to travel between all grazings.

The next $NN$ lines contain $xx$, $yy$, and $tt$ $(-{10}^9\le x,y\le {10}^9;0\le t\le {10}^9)(-10^9\; \backslash le\; x,\; y\; \backslash le\; 10^9;\; 0\; \backslash le\; t\; \backslash le\; 10^9)$ separated by a space describing the location and time of each cow's alibi.

출력

Output a single integer: the number of cows with alibis that prove their innocence.

2 4
0 0 100
50 0 200
0 50 50
1000 1000 0
50 0 200
10 0 170

2