22194_Pos

We have a warehouse, which is H feet height and W feet width, with solid north and south walls. The east and west walls have sliding doors which allow trucks free entry and exit. We want to drive big trucks in a straight line into the warehouse through the west wall and (after unloading and without changing direction) out through the east wall. Unfortunately the roof is supported by posts.

Take the positions and sizes of the posts as inputs and output the width of the widest truck that can drive straight through without touching any posts (or the north or south wall).

The first line contains three integers n, W, H. 1 ≤ n ≤ 30,  1 ≤ W, H ≤ 10000. The following n lines describe n posts. Each contains three real numbers x, y, r.  0 < x < W,  0 < y < H,  0 < r. The posts do not intersect with each other (or the walls).

For each ease, output a line contains a real number with precision up to two decimal places.

2 100 100
50 25 5
50 75 10

35.00