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Crime

Time limit2sMemory limit512 MB

Summary
Given time T and walking and car speeds W and C on one straight road, compute the area of the region where the suspect could be.
Level

Medium7 of 10

Topics
Math, Geometry, Combinatorics
Solved
No attempts yet

Problem

Tamir is the best detective in his city. Today a crime took place in his city. Information arrived that the suspect was last seen on a road in the city. T seconds have now passed since that information arrived, and before starting his operation Tamir must first find the area of the region where the suspect could be. Cars in Tamir's city can drive only on roads, and the city has exactly one road, an infinitely long straight line. The suspect can travel on foot at up to W m/s and by car at up to C m/s, a car can be found anywhere on the road, and getting in or out of a car takes no time.

Your task is to find for Tamir the area of the region where the suspect could be.

Input

The first line contains an integer N, the number of tests. N ≤ 100

Each of the next N lines contains the integers T, W, C. 1 ≤ T, W, C ≤ 100

Output

For each test, print the corresponding answer, the area in m2, with 3 digits of precision after the decimal point.

Examples1

  1. Example 1

    Input
    2
    1 1 1
    1 1 2
    
    Expected output
    3.142
    4.511