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.util.*;
import java.io.*;
 
public class Main {
	static InputReader scn = new InputReader(System.in);
	static OutputWriter out = new OutputWriter(System.out);
	public static void main(String[] args) {
		// Running Number Of TestCases (t)
		int t = 1;
		while(t-- > 0)
			solve();
		out.close();
	}

	public static void dummy(){
		// Dummy Code for Rough
		int n = scn.nextInt();
		out.println(n);
	}
	static boolean[] dp;
	public static void solve() {
		// Main Solution (AC)
		double a = scn.nextInt();
		double b = scn.nextInt();
		int locations = scn.nextInt();
		double ans = Double.MAX_VALUE;
		while(locations-- > 0){
			double x = scn.nextInt();
			double y = scn.nextInt();
			double v = scn.nextInt();
			double x2 = (x - a) * (x - a);
			double y2 = (y - b) * (y - b);
			double dist = (double) Math.sqrt(x2 + y2);
			dist /= v;
			ans = Math.min(ans, dist);
		}
		out.println(ans);
		
	}
	// [123, 168, 714, 868, 987]
	public static int Check(int arr[], int l, int r, int x, int n) {
		if (r >= l) {
			int mid = l + (r - l) / 2;
			if (mid == 0 || mid == n-1 || (arr[mid] <= x && arr[mid+1] > x)) 
				return mid;
			else if (arr[mid] <= x)
				return Check(arr, mid, r, x, n);
			else return Check(arr, l, mid, x, n);
		}
		return -1;
	}

	public static HashMap<Integer, Integer> CountFrequencies(int[] arr) {

		HashMap<Integer, Integer> map = new HashMap<>();
		map.put(0, 0);
		map.put(1, 0);
		for (int i : arr) {
			if (map.containsKey(i))
				map.put(i, map.get(i) + 1);
			else
				map.put(i, 1);
		}
		return map;
	}

	public static HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        List<Map.Entry<Integer, Integer> > list = new LinkedList<Map.Entry<Integer, Integer> >(hm.entrySet());
        Collections.sort(list, new Comparator<Map.Entry<Integer, Integer> >() { 
            public int compare(Map.Entry<Integer, Integer> o1,  
                               Map.Entry<Integer, Integer> o2){ 
                return (o1.getValue()).compareTo(o2.getValue()); 
            } 
        });
        HashMap<Integer, Integer> temp = new LinkedHashMap<Integer, Integer>(); 
        for (Map.Entry<Integer, Integer> aa : list) { 
            temp.put(aa.getKey(), aa.getValue()); 
        } 
        return temp; 
    } 

	public static void sortbyColumn(int[][] arr, int col) {
		Arrays.sort(arr, new Comparator<int[]>() {
			public int compare(final int[] entry1, final int[] entry2) {
				if (entry1[col] > entry2[col])
					return 1;
				else
					return -1;
			}
		});
	}
 
	public static HashSet<Long> primeFactors(long n, HashSet<Long> list, int d) {
		list.add(1L);
		list.add(n);
		for (long i = 2; i <= Math.sqrt(n); i += 1) {
			long a = i;
			if (n % a == 0) {
				list.add(a);
				if (n % (n / a) == 0)
					list.add(n / a);
			}
		}
		return list;
	}
 
	public static void ArraySort2D(int[][] arr, int xy) {
		// xy == 0, for sorting wrt X-Axis
		// xy == 1, for sorting wrt Y-Axis
		Arrays.sort(arr, Comparator.comparingDouble(o -> o[xy]));
	}
 	
 	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}
 	
 	public static int binarySearch(int arr[], int l, int r, int x) {
		if (r >= l) {
			int mid = l + (r - l) / 2;
			if (arr[mid] == x)
				return mid;
			if (arr[mid] > x)
				return binarySearch(arr, l, mid - 1, x);
			return binarySearch(arr, mid + 1, r, x);
		}
		return -1;
	}
 
	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int[] readArrays(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = scn.nextInt();
			}
			return a;
		}
 
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		public String next() {
			return nextLine();
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
 
	static class OutputWriter {
		private final PrintWriter writer;
 
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
 
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
 
		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0) {
					writer.print(' ');
//                    writer.print(1);
				}
				writer.print(objects[i]);
			}
		}
 
		public void println(Object... objects) {
			print(objects);
			writer.println();
		}
 
		public void close() {
			writer.close();
		}
	}
 
}