Vasiliy lives at point (a, b) of the coordinate plane. He is hurrying up to work so he wants to get out of his house as soon as possible. New app suggested n available Beru-taxi nearby. The i-th taxi is located at point (xi, yi) and moves with a speed vi. 

Consider that each of n drivers will move directly to Vasiliy and with a maximum possible speed. Compute the minimum time when Vasiliy will get in any of Beru-taxi cars.

Input

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

The second line contains a single integer n (1 ≤ n ≤ 1000) — the number of available Beru-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 located at exactly the same point where Vasiliy lives.

Output

Print a single real value — the minimum time Vasiliy needs to get in any of the Beru-taxi cars. You answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

0 0
2
2 0 1
0 2 2


Output

1.00000000000000000000

Input

1 3
3
3 3 2
-2 3 6
-2 7 10


Output

0.50000000000000000000

Note

In the first sample, first taxi will get to Vasiliy in time 2, and second will do this in time 1, therefore 1 is the answer.

In the second sample, cars 2 and 3 will arrive simultaneously.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Set;

public class CF66 {

	static BufferedReader br;

	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		
		int[]arr=readIntArr();
		int a=arr[0];
		int b=arr[1];
		int n=readInt();
		double tm=Integer.MAX_VALUE;
		for(int i=0;i<n;i++){
			arr=readIntArr();
			int dist=a-arr[0];
			dist*=dist;
			int d2=b-arr[1];
			d2*=d2;
			
			double d=Math.sqrt(dist+d2);
		
			d/=arr[2];
			//System.out.println(d);
			tm=Math.min(d, tm);
		}
		
		System.out.println(tm);
		br.close();

	}

	

	static public String readString() throws IOException {
		return br.readLine();

	}

	static public long readLong() throws IOException {
		return Long.parseLong(br.readLine());
	}

	static public int readInt() throws IOException {
		return Integer.parseInt(br.readLine());
	}

	static public int[] readIntArr() throws IOException {
		String[] str = br.readLine().split(" ");
		int arr[] = new int[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Integer.parseInt(str[i]);
		return arr;
	}

	static public Integer[] readOIntArr() throws IOException {
		String[] str = br.readLine().split(" ");
		Integer arr[] = new Integer[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = new Integer(str[i]);
		return arr;
	}

	static public double[] readDoubleArr() throws IOException {
		String[] str = br.readLine().split(" ");
		double arr[] = new double[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Double.parseDouble(str[i]);
		return arr;
	}

	static public Double[] readODoubleArr() throws IOException {
		String[] str = br.readLine().split(" ");
		Double arr[] = new Double[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = new Double(str[i]);
		return arr;
	}

	static public long[] readLongArr() throws IOException {
		String[] str = br.readLine().split(" ");
		long arr[] = new long[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = Long.parseLong(str[i]);
		return arr;
	}

	static public Long[] readOLongArr() throws IOException {
		String[] str = br.readLine().split(" ");
		Long arr[] = new Long[str.length];
		for (int i = 0; i < arr.length; i++)
			arr[i] = new Long(str[i]);
		return arr;
	}

	static public double readDouble() throws IOException {
		return Double.parseDouble(br.readLine());
	}
}