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Click the Lines
Time Limit: 5000MSMemory Limit: 65536K
Total Submissions: 254Accepted: 75


In many graphic drawing applications, you can click on a line object. A well-known approach to detect if a line is clicked by a mouse is to compute the distance between the click position and the line. For example, in Figure 1, the line is said to be selected if the distance d is less than a threshold D (dD).

Give you a set of lines (with equation of the form ax + by + c = 0), please compute the minimum clicks to select all the lines. For example, to select two lines, the minimum number of clicks is one, that is, you can make a click near the cross point of the two lines.

Note: In the test data, each line at least intersects with another line.


The first line of input data begins with a number N the number of test cases. Each test case begins with two integers L and D, where L (L ≤ 200) is the number of lines and D (D > 0) is the threshold for testing if a line is selected. The data of lines listed one by one. Each line is represented by (ax + by + c = 0). The three floating numbers a, b, c, separated by space are given to represent the line.


Please output the minimum number of clicks in a new line for each test case.

Sample Input

2 5
0 1 0
1 0 0
3 1
0 1 0
1 0 0
1 1 2

Sample Output



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