Salma lives at points (a, b) of the coordinate plane. She needs more time to go to her work. The yellow taxi has an application that suggests n available cars nearby. The i-th taxi is located at point (xi, yi) and moves with speed vi.

Suppose that each n driver will move directly to Salam at the maximum possible speed. Compute the minimum time when Salam will get in any of the Yellow Taxi cars.

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Input Format

The first line of the input contains two integers a and b ( - 100 a, b 100) coordinates of Salam's home.

The second line contains a single integer n (1 n 1000) the number of available yellow Taxi cars nearby.

The i-th of the following n lines contains three integers xi, yi, and vi ( - 100 xi, yi 100, 1 vi 100) the coordinates of the i-th car and its speed.

It's allowed that several cars are located at the same point. Also, cars may be found at exactly the same point where Salam lives.

Constraints

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Output Format

Print a single real value the minimum time Salam needs to get in any of the Yellow Taxi cars. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Sample Input 0

0 0 2 2 0 1 0 2 2 Sample Output 0

1.00000000000000000000 Sample Input 1

1 3 3 3 3 2 -2 3 6 -2 7 10 Sample Output 1

0.50000000000000000000

Simple java solution.