Problem: One warm and sunny day king Copa decided to visit the shooting gallery, located at the Central Park, and try to win the main prize — big pink plush panda. The king is not good at shooting, so he invited you to help him.

The shooting gallery is an infinite vertical plane with Cartesian coordinate system on it. The targets are points on this plane. Each target is described by it's coordinates xi, and yi, by the time of it's appearance ti and by the number pi, which gives the probability that Copa hits this target if he aims at it.

A target appears and disappears instantly, so Copa can hit the target only if at the moment ti his gun sight aimed at (xi, yi). Speed of movement of the gun sight on the plane is equal to 1. Copa knows all the information about the targets beforehand (remember, he is a king!). He wants to play in the optimal way, which maximizes the expected value of the amount of hit targets. He can aim at any target at the moment 0.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — amount of targets in the shooting gallery. Then n lines follow, each describing one target. Each description consists of four numbers xi, yi, ti, pi (where xi, yi, ti — integers,  - 1000 ≤ xi, yi ≤ 1000, 0 ≤ ti ≤ 109, real number pi is given with no more than 6 digits after the decimal point, 0 ≤ pi ≤ 1). No two targets may be at the same point.

Output

Output the maximum expected value of the amount of targets that was shot by the king. Your answer will be accepted if it differs from the correct answer by not more than 10 - 6.

Examples

Input

1
0 0 0 0.5


Output

0.5000000000


Input

2
0 0 0 0.6
5 0 5 0.7


Output

1.3000000000

Solution (in JAVA):

Solution:

import java.io.*;

import java.util.*;



/*



*/


 
 
public class P2 {
	static FastReader sc=null;
	
	public static void main(String[] args) {
		sc=new FastReader();
		int n=sc.nextInt();
		Pair p[]=new Pair[n];
		for(int i=0;i<n;i++)p[i]=new Pair(sc.nextInt(),sc.nextLong(),sc.nextLong(),sc.nextDouble());
		
		Arrays.sort(p);
		
		double dp[]=new double[n];
		for(int i=0;i<n;i++)dp[i]=p[i].p;
		
		//MAX EXPECTED VALUE ENDING AT I
		
		for(int i=1;i<n;i++) {
			for(int j=0;j<i;j++) {
				///PICK THIS
				if(go(p,i,j))dp[i]=Math.max(dp[j]+p[i].p,dp[i]);
			}
		}
		
		double ans=0;
		for(double e:dp)ans=Math.max(e, ans);
		
		System.out.println(ans);
		
		
		
	}
	static boolean go(Pair p[],int i,int j) {
		
		double dist=Math.abs(p[i].x-p[j].x)*Math.abs(p[i].x-p[j].x)+
				Math.abs(p[i].y-p[j].y)*Math.abs(p[i].y-p[j].y);
		
		
		double t=Math.abs(p[j].t-p[i].t)*Math.abs(p[j].t-p[i].t);
		
		return Double.compare(dist, t)<=0;
		
	}
	static class Pair implements Comparable<Pair>{
		long x,y;
		long t;
		double p;
		Pair(long x,long y,long t,double p){
			this.x=x;
			this.y=y;
			this.t=t;
			this.p=p;
		}
		@Override
		public int compareTo(Pair o) {
			return Long.compare(this.t, o.t);
		}
	}

	
	
	
	
	
	
	static void reverseSort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i:a)al.add(i);
		Collections.sort(al,Collections.reverseOrder());
		for(int i=0;i<a.length;i++)a[i]=al.get(i);
	}
	static int gcd(int a,int b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}
	static long gcd(long a,long b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}
	static void reverse(int a[]) {
		int n=a.length;
		int b[]=new int[n];
		for(int i=0;i<n;i++)b[i]=a[n-1-i];
		for(int i=0;i<n;i++)a[i]=b[i];
	}
	static void reverse(char a[]) {
		int n=a.length;
		char b[]=new char[n];
		for(int i=0;i<n;i++)b[i]=a[n-1-i];
		for(int i=0;i<n;i++)a[i]=b[i];
	}
	static void ruffleSort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i:a)al.add(i);
		Collections.sort(al);
		for(int i=0;i<a.length;i++)a[i]=al.get(i);
	}
	
	
	
	static void print(int[] a) {
		for(int e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	static void print(long a[]) {
		for(long e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	
	
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
        int[] readArray(int n) {
    		int a[]=new int [n];
    		for(int i=0;i<n;i++) {
    			a[i]=sc.nextInt();
    		}
    		return a;
    	}
        long[] readArrayL(int n) {
    		long a[]=new long [n];
    		for(int i=0;i<n;i++) {
    			a[i]=sc.nextLong();
    		}
    		return a;
    	}
    } 
}