It is necessary to watch stars with the partner in passionate love. So Jack and Rose decide to watch stars this night.

In the sky, there are n stars in a rectangular Cartesian coordinate system and they have a special camera fixed in one position. This camera contains two different circles which are internally tangent. And it has a magic viewfinder which can be treated as a circle with dynamic size between the two circles (externally tangent to the small one and internally tangent to the large one) as shown in figure below. The stars in the range of the viewfinder (not on the edge) would be photographed. The problem is, what is the maximum number of stars could be photographed in one photograph?

The first line contains an integer  () --- the number of test cases.

The first line of each test case contains three integers ,  and  (, ) --- the number of stars, the radius of the large circle and the radius of the small circle.

The next n lines contain the coordinates of the stars, where the -th line contains two integers ,  () --- the coordinates of the -th star.

It's guaranteed that  and , and all  are pairwise different.

Output one integer in one line for each test case --- the maximum number of stars in one photograph.

1
6 5 2
4 3
6 2
6 -3
3 -4
7 4
8 -3

3