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.*;
    import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
 
 
 
     
     
    public  class Main {
    	public static InputReader in;
        public static PrintWriter pw;
     
     
     
    	public static void main(String args[]) 
    	{
    		new Thread(null, new Runnable() {
                public void run() {
                    try{
                        solve();
                    }
                    catch(Exception e){
                        e.printStackTrace();
                    }
                }
            }, "1", 1 << 26).start();
        }
    	static ArrayList<Integer> g[];
    	static ArrayList<Integer> h[];
    	static boolean visited[];
    	static int[] parent;
    	static int par[];
    	static int degree[];
    	static int edjes=0;
    	static int start=-1;
    	static int end=-1;
    	static int Total=0;
    	static int time1[];
    	static int time2[];
    	static int glob=0;
    	static int[] ans;
    	static boolean vis2[][];
    	//static long sum1=0;
    	//static long val[];
        static ArrayList<Integer> levels[];
        static int max=0;
        static int lev=1;
        static ArrayList<Integer> nodes[];
        static ArrayList<Integer> values[];
        static int depth[];
        static boolean found=false;
       // static long sm[];
        static int sum1=0;
        static int pre[][];
        static int subtree[];
       static  int cnt=0;
       static  HashMap<String,Integer> hm;
       static int sm[];
       static int size[];
       static long mul[];
       static long d[]=new long[1000000];
       static int tot=0;
       static long highest=(long)1e9;
       static boolean bit=false;
        static Stack<Integer> tt=new Stack();
       static HashSet<String> set=new HashSet<String>();
 	   static long fact[],num[];
 	   static long MOD=1000000007;
 	   static int value[];static int premen[];
 	   static int count=0,index=0;
 	   static double ans11[];
 	   static int price[];
 	   static ArrayList<String> hp[][];
 	   static boolean visit[][];
 	   static int cnu[]=new int[1000001];
 	   static int label=1;
 	   static int his[][];
 	   static int size1=0;
 	   static int up[],down[];
 	   static int TotalUp=0;
 	   static long dist[];
 	//   static HashMap<String,Integer> hm1=new HashMap();
 	  // static HashMap<Integer,Integer> hm2=new HashMap();
 	   static TreeSet<Long> set1=new TreeSet();
 	  static  long DP[][][]=new long[20][200][1500];
 	 	static int t=-1,n=-1;
 	 	static int two[],min[],r[];
 	 	static int total[];static int black[];
 	 	static int Parent[];
 	 	static int subtree1[][];
 	 	static int tin[],tout[],a[];
 	 public static void solve() throws FileNotFoundException{
    		
    	
    		 in = new InputReader(System.in);
    		 pw = new PrintWriter(System.out);  
    	/*	 String p=in.readString();
    	     char c[]=p.toCharArray();
    	     int z[]=new int[p.length()];
    	     z[0]=0;
    	     int left=0;
    	     int right=0;
    	     for(int i=1;i<p.length();i++)
    	     {
    	    	 if(i>right)
    	    	 {
    	    		 
    	    		 left=right=i;
    	    		 while(right<p.length()&&c[right]==c[right-left])
    	    			 right++;
    	    		 z[i]=right-left;
    	    		 right--;
    	    	 }
    	    	 else
    	    	 {
    	    		 int k=i-left;
    	    		 if(z[k]<right-i+1)
    	    		 {
    	    			 z[i]=z[k];
    	    		 }
    	    		 else
    	    		 {
    	    			 left=i;
    	    			 while(right<p.length()&&c[right]==c[right-left])
        	    			 right++;
        	    		 z[i]=right-left;
        	    		 right--;
    	    		 }
    	    	 }
    	    	  
    	     }*/
    		 int a=in.nextInt();int b=in.nextInt();
    		 int t=in.nextInt();
    		 double ans=Double.MAX_VALUE;
    		 while(t-->0)
    		 {
    			 int x=in.nextInt();
    			 int y=in.nextInt();
    			 double o=Math.abs((x-a)*(x-a));
    			 double p=Math.abs((b-y)*(b-y));
    			 o+=p;
    			 double fk=(double)Math.sqrt(o);
    			 int v=in.nextInt();
    			 fk/=(double)v;
    			 if(ans>fk)
    				 ans=fk;
    		 }
    		 System.out.printf("%.10f",ans);
 	 }
 	 static int Par[]=new int[202];
 	 public static void Height(int cur,int par){
 		 Par[cur]=par;
 		 visited[cur]=true;
 		 int t=0;
 		 for(int x:g[cur])
 		 {
 			 if(!visited[x])
 			 { 
 				 t++;
 				 Height(x,cur);
 				 high[cur]=Math.max(high[cur], high[x]+1);
 			 }
 		 }
 		 if(t==0)
 		 {
 			 high[cur]=0;
 		 }
 	
 	 }
 	 static int dia[]=new int[202];
 	 static int high[]=new int[292];
 	 public static void Diameter(int curr,int parent)
 	 {
 		visited[curr]=true;
 		int trees=0;
 		ArrayList<Integer> set=new ArrayList();
 	
 		for(int x:g[curr])
 		{
 			if(!visited[x])
 			{
 				trees++;
 				Diameter(x,curr);
 				dia[curr]=Math.max(dia[curr],high[x]);
 				set.add(high[x]);
 			}
 		}
 		if(set.size()>=2)
 		{
 			Collections.sort(set,Collections.reverseOrder());
 			dia[curr]=Math.max(dia[curr],set.get(0)+set.get(1)+2);
 		}
 		else if(set.size()>0)
 		{
 			dia[curr]=Math.max(dia[curr],set.get(0)+1);
 		}
 		if(trees==0)
 		{
 			dia[curr]=0;
 		}

 	 }
 	 
      	 
 	 public static boolean IsPal(String s)
 	 {
 		 char c[]=s.toCharArray();
 		 for(int i=0;i<c.length/2;i++)
 		 {
 			 if(c[i]!=c[s.length()-1-i])
 				 return false;
 		 }
 		 return true;
 	 }
 	public static void Merge(long[] a,int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
    public static void Merge_Array(long a[],int p,int q,int r){
       long b[] = new long[q-p+1];
        long c[] = new long[r-q];
        for(int i=0;i<b.length;i++)
            b[i] = a[p+i];
        for(int i=0;i<c.length;i++)
            c[i] = a[q+i+1];
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                a[k] = c[j];
                j++;
            }
            else if(j==c.length){
                a[k] = b[i];
                i++;
            }
            else if(b[i]<c[j]){
                a[k] = b[i];
                i++;
            }
            else{
                a[k] = c[j];
                j++;
            }
        }
    }
 	 
 	 
 	 
 	
 	
       
 	  public static void dfs1(int curr,int parent)
 	  {
 		  visited[curr]=true;
 		  
 		  for(int x:g[curr])
 		  {
 			  
 			  if(x==parent)continue;
 			  depth[x]=depth[curr]+1;
 			  up[x]=up[curr];
 			  if(h[x].contains(curr)){
 				  up[x]++;
 				  TotalUp++;
 			  }
 			  dfs1(x,curr);
 		  }
 	  }
 	 
        
        
        public static void dfs(int curr,int Parent)
        {
        	visited[curr]=true;
        	size[curr]=1;
        	parent[curr]=Parent;
        	count++;
        	if(value[curr]>0)
        	{
        		index=value[curr];
        	}
        	for(int x:g[curr])
        	{
        		if(!visited[x])
        		{
        			dfs(x,curr);
        			size[curr]+=size[x];
        		}
        	}
        }
        static long ncr(long a, long b){
			if(b>a || b<0) return 0;
			long f = (fact[(int) a]*modInverse(((fact[(int) b]*fact[(int) (a-b)])%MOD), MOD))%MOD;
			return f;
		}
		static long modInverse(long a, long mOD2){
            return  power(a, mOD2-2, mOD2);
}
static long power(long x, long y, long m)
{
    if (y == 0)
        return 1;
    long p = power(x, y/2, m) % m;
    p = (p * p) % m;
 
    return (y%2 == 0)? p : (x * p) % m;
}
 
        public static long gcd(long x, long y) {
    		if (x == 0)
    			return y;
    		else
    			return gcd( y % x,x);
    	}	
        public static long power(long a,long b)
		{
			long result=1;
			while(b>0)
			{
				if(b%2==1)
					result*=a;
				a=a*a;
				b/=2;
			}
			return result;
		}
        static class Pair implements Comparable<Pair>{
        	//int index;
        		String s;
        		int m;
        		//int index;
        	//	int h;
        		Pair(String index,int value){
        	     	this.s=index;
        			this.m=value;
        		}
        		@Override
        		public int compareTo(Pair o) {
                          return s.length()-o.s.length();
        		}
        				
        	}
    	static class InputReader {
     
    		private InputStream stream;
    		private byte[] buf = new byte[8192];
    		private int curChar, snumChars;
    		private SpaceCharFilter filter;
     
    		public InputReader(InputStream stream) {
    			this.stream = stream;
    		}
     
    		public int snext() {
    			if (snumChars == -1)
    				throw new InputMismatchException();
    			if (curChar >= snumChars) {
    				curChar = 0;
    				try {
    					snumChars = stream.read(buf);
    				} catch (IOException e) {
    					throw new InputMismatchException();
    				}
    				if (snumChars <= 0)
    					return -1;
    			}
    			return buf[curChar++];
    		}
     
    		public   int nextInt() {
    			int c = snext();
    			while (isSpaceChar(c))
    				c = snext();
    			int sgn = 1;
    			if (c == '-') {
    				sgn = -1;
    				c = snext();
    			}
    			int res = 0;
    			do {
    				if (c < '0' || c > '9')
    					throw new InputMismatchException();
    				res *= 10;
    				res += c - '0';
    				c = snext();
    			} while (!isSpaceChar(c));
    			return res * sgn;
    		}
     
    		public long nextLong() {
    			int c = snext();
    			while (isSpaceChar(c))
    				c = snext();
    			int sgn = 1;
    			if (c == '-') {
    				sgn = -1;
    				c = snext();
    			}
    			long res = 0;
    			do {
    				if (c < '0' || c > '9')
    					throw new InputMismatchException();
    				res *= 10;
    				res += c - '0';
    				c = snext();
    			} while (!isSpaceChar(c));
    			return res * sgn;
    		}
     
    		public int[] nextIntArray(int n) {
    			int a[] = new int[n];
    			for (int i = 0; i < n; i++)
    				a[i] = nextInt();
    			return a;
    		}
     
    		public String readString() {
    			int c = snext();
    			while (isSpaceChar(c))
    				c = snext();
    			StringBuilder res = new StringBuilder();
    			do {
    				res.appendCodePoint(c);
    				c = snext();
    			} 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 interface SpaceCharFilter {
    			public boolean isSpaceChar(int ch);
    		}
    	}
    }
 