There are some circles on a plane. They may intersect or overlap.You are to place a circle q on this plane (its radium is fixed) and want to cover the maximum possible number of circles. A circle is covered by q if it lies fully inside q.
Input:
This problem contains multiple test cases! Each test case begins with a real number r(r tells the radium of q) and a positive number n(0<n<100,the number of circles on the plane).Then follows n lines ,each describe a circle. Each of the following line contains three real number , the first two describe the x-ax and y-ax of the center of circle,the last one represents for the radium of this circle. Input terminates with the EOF(end of file).
Output:
Output one integer telling the maximum number of circles q can cover in one line for each test case.
Sample Input:
2.0 1
0.0 0.0 2.0
4.0 2
0.0 0.0 2.0
0.0 1.0 1.0
Sample Output:
1
2
