문제

Note: The time limit for this problem is 4s, two times the default.

Somebody has been grazing in Farmer John's $(1 \le G \le 10^5)$ 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 $N$ $(1 \le N \le 10^5)$ 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 $G$ and $N$ separated by a space.

The next $G$ lines contain the integers $x$, $y$, and $t$ $(-10^9 \le x, y \le 10^9; 0 \le t \le 10^9)$ 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 $N$ lines contain $x$, $y$, and $t$ $(-10^9 \le x, y \le 10^9; 0 \le t \le 10^9)$ 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.

예제 입력 1

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

예제 출력 1

2

점수

Inputs 2-4: $1 \le G, N \le 10^3$. Also, for both the fields and alibis, $-10^6 \le x, y \le 10^6$ and $0 \le t \le 10^6$. Inputs 5-11: No additional constraints.