You are given three integers A,B and C.
 We choose two real numbers x and y such that 0 ≤ x ≤ A and 0 ≤ y ≤ B.
 What is the probability that x+y≤C ?


Input
The first line of input contains T denoting the number of test cases.
Each of the following T lines contains three space separated Integers A,B and C

Output
For each test case, output a single line containing the required probablity.

Constraints
1 ≤ T ≤ 10^5 
0 ≤ A,B ≤ 10^9 
0 ≤ C ≤ 10^18 

Example
Input:

2
4 10 3
4 10 11


Output:

0.1125
0.8875


NOTE: Your answer will be accepted if the absolute error is less than 10^-6.

Source: codechef | Difficulty: UNKNOWN_DIFFICULTY


Solutions: