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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Random;
import java.util.StringTokenizer;

public class _30C {

  static int n;
  static int[] x, y, t;
  static double[] p;
  static Random rand = new Random();

  static void sort(int l, int r) {
    int i = l, j = r, cb = t[rand.nextInt(r - l + 1) + l];
    do {
      while (t[i] < cb)
        i++;
      while (t[j] > cb)
        j--;
      if (i <= j) {
        ArrayUtil.swap(x, i, j);
        ArrayUtil.swap(y, i, j);
        ArrayUtil.swap(t, i, j);
        ArrayUtil.swap(p, i, j);
        i++;
        j--;
      }
    } while (i <= j);

    if (i < r)
      sort(i, r);
    if (j > l)
      sort(l, j);
  }

  static long sqr(long x) {
    return x * x;
  }

  public static void main(String[] args) throws Exception {
    Reader.init(System.in);
    BufferedWriter cout = new BufferedWriter(new OutputStreamWriter(System.out));

    n = Reader.nextInt();
    x = new int[n];
    y = new int[n];
    t = new int[n];
    p = new double[n];
    for (int i = 0; i < n; i++) {
      x[i] = Reader.nextInt();
      y[i] = Reader.nextInt();
      t[i] = Reader.nextInt();
      p[i] = Reader.nextDouble();
    }
    sort(0, n - 1);

    double[] f = new double[n];
    for (int i = 0; i < n; i++) {
      f[i] = p[i];
      for (int j = 0; j < i; j++)
        if (sqr(t[i] - t[j]) >= sqr(x[i] - x[j]) + sqr(y[i] - y[j]))
          f[i] = Math.max(f[i], f[j] + p[i]);
    }

    double ans = -1;
    for (int i = 0; i < f.length; i++)
      if (f[i] > ans)
        ans = f[i];
    System.out.printf("%.10f%n", ans);

    cout.close();
  }

  static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
    final U _1;
    final V _2;

    private Pair(U key, V val) {
      this._1 = key;
      this._2 = val;
    }

    public static <U extends Comparable<U>, V extends Comparable<V>> Pair<U, V> instanceOf(U _1, V _2) {
      return new Pair<U, V>(_1, _2);
    }

    @Override
    public String toString() {
      return _1 + " " + _2;
    }

    @Override
    public int hashCode() {
      int res = 17;
      res = res * 31 + _1.hashCode();
      res = res * 31 + _2.hashCode();
      return res;
    }

    @Override
    public int compareTo(Pair<U, V> that) {
      int res = this._1.compareTo(that._1);
      if (res < 0 || res > 0)
        return res;
      else
        return this._2.compareTo(that._2);
    }

    @Override
    public boolean equals(Object obj) {
      if (this == obj)
        return true;
      if (!(obj instanceof Pair))
        return false;
      Pair<?, ?> that = (Pair<?, ?>) obj;
      return _1.equals(that._1) && _2.equals(that._2);
    }
  }

  /** Class for buffered reading int and double values */
  static class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
      reader = new BufferedReader(new InputStreamReader(input));
      tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
      while (!tokenizer.hasMoreTokens()) {
        // TODO add check for eof if necessary
        tokenizer = new StringTokenizer(reader.readLine());
      }
      return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
      return Integer.parseInt(next());
    }

    static double nextDouble() throws IOException {
      return Double.parseDouble(next());
    }
  }

  static class ArrayUtil {
    static void swap(int[] a, int i, int j) {
      int tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(long[] a, int i, int j) {
      long tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(double[] a, int i, int j) {
      double tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(char[] a, int i, int j) {
      char tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void swap(boolean[] a, int i, int j) {
      boolean tmp = a[i];
      a[i] = a[j];
      a[j] = tmp;
    }

    static void reverse(int[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(long[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(double[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(char[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static void reverse(boolean[] a, int i, int j) {
      for (; i < j; i++, j--)
        swap(a, i, j);
    }

    static long sum(int[] a) {
      int sum = 0;
      for (int i : a)
        sum += i;
      return sum;
    }

    static long sum(long[] a) {
      long sum = 0;
      for (long i : a)
        sum += i;
      return sum;
    }

    static double sum(double[] a) {
      double sum = 0;
      for (double i : a)
        sum += i;
      return sum;
    }

    static int max(int[] a) {
      int max = Integer.MIN_VALUE;
      for (int i : a)
        if (i > max)
          max = i;
      return max;
    }

    static int min(int[] a) {
      int min = Integer.MAX_VALUE;
      for (int i : a)
        if (i < min)
          min = i;
      return min;
    }

    static long max(long[] a) {
      long max = Long.MIN_VALUE;
      for (long i : a)
        if (i > max)
          max = i;
      return max;
    }

    static long min(long[] a) {
      long min = Long.MAX_VALUE;
      for (long i : a)
        if (i < min)
          min = i;
      return min;
    }
  }
}