Problem: Suppose that there are some light sources and many spherical balloons. All light sources have sizes small enough to be modeled as point light sources, and they emit light in all directions. The surfaces of the balloons absorb light and do not reflect light. Surprisingly in this world, balloons may overlap.

You want the total illumination intensity at an objective point as high as possible. For this purpose, some of the balloons obstructing lights can be removed. Because of the removal costs, however, there is a certain limit on the number of balloons to be removed. Thus, you would like to remove an appropriate set of balloons so as to maximize the illumination intensity at the objective point.

The following figure illustrates the configuration specified in the first dataset of the sample input given below. The figure shows the xy-plane, which is enough because, in this dataset, the z-coordinates of all the light sources, balloon centers, and the objective point are zero. In the figure, light sources are shown as stars and balloons as circles. The objective point is at the origin, and you may remove up to 4 balloons. In this case, the dashed circles in the figure correspond to the balloons to be removed.

<image>

Figure G.1: First dataset of the sample input.



Input

The input is a sequence of datasets. Each dataset is formatted as follows.

N M R
S1x S1y S1z S1r
...
SNx SNy SNz SNr
T1x T1y T1z T1b
...
TMx TMy TMz TMb
Ex Ey Ez


The first line of a dataset contains three positive integers, N, M and R, separated by a single space. N means the number of balloons that does not exceed 2000. M means the number of light sources that does not exceed 15. R means the number of balloons that may be removed, which does not exceed N.

Each of the N lines following the first line contains four integers separated by a single space. (Six, Siy, Siz) means the center position of the i-th balloon and Sir means its radius.

Each of the following M lines contains four integers separated by a single space. (Tjx, Tjy, Tjz) means the position of the j-th light source and Tjb means its brightness.

The last line of a dataset contains three integers separated by a single space. (Ex, Ey, Ez) means the position of the objective point.

Six, Siy, Siz, Tjx, Tjy, Tjz, Ex, Ey and Ez are greater than -500, and less than 500. Sir is greater than 0, and less than 500. Tjb is greater than 0, and less than 80000.

At the objective point, the intensity of the light from the j-th light source is in inverse proportion to the square of the distance, namely

Tjb / { (Tjx − Ex)2 + (Tjy − Ey)2 + (Tjz − Ez)2 },

if there is no balloon interrupting the light. The total illumination intensity is the sum of the above.

You may assume the following.

1. The distance between the objective point and any light source is not less than 1.
2. For every i and j, even if Sir changes by ε (|ε| < 0.01), whether the i-th balloon hides the j-th light or not does not change.


The end of the input is indicated by a line of three zeros.

Output

For each dataset, output a line containing a decimal fraction which means the highest possible illumination intensity at the objective point after removing R balloons. The output should not contain an error greater than 0.0001.

Example

Input

12 5 4
0 10 0 1
1 5 0 2
1 4 0 2
0 0 0 2
10 0 0 1
3 -1 0 2
5 -1 0 2
10 10 0 15
0 -10 0 1
10 -10 0 1
-10 -10 0 1
10 10 0 1
0 10 0 240
10 0 0 200
10 -2 0 52
-10 0 0 100
1 1 0 2
0 0 0
12 5 4
0 10 0 1
1 5 0 2
1 4 0 2
0 0 0 2
10 0 0 1
3 -1 0 2
5 -1 0 2
10 10 0 15
0 -10 0 1
10 -10 0 1
-10 -10 0 1
10 10 0 1
0 10 0 260
10 0 0 200
10 -2 0 52
-10 0 0 100
1 1 0 2
0 0 0
5 1 3
1 2 0 2
-1 8 -1 8
-2 -3 5 6
-2 1 3 3
-4 2 3 5
1 1 2 7
0 0 0
5 1 2
1 2 0 2
-1 8 -1 8
-2 -3 5 6
-2 1 3 3
-4 2 3 5
1 1 2 7
0 0 0
0 0 0


Output

3.5
3.6
1.1666666666666667
0.0

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) {
		IO io = new IO();
		while(true) {
			int n = io.nextInt();
			int m = io.nextInt();
			int r = io.nextInt();
			if (n == 0) {
				break;
			}
			Vector3.Long[] sx = new Vector3.Long[n];
			long[] sr = new long[n];
			for(int i=0;i<n;i++) {
				sx[i] = new Vector3.Long(io.nextLong(), io.nextLong(), io.nextLong());
				sr[i] = io.nextLong();
			}
			Vector3.Long[] tx = new Vector3.Long[m];
			long[] tb = new long[m];
			for(int i=0;i<m;i++) {
				tx[i] = new Vector3.Long(io.nextLong(), io.nextLong(), io.nextLong());
				tb[i] = io.nextLong();
			}
			Vector3.Long ex = new Vector3.Long(io.nextLong(), io.nextLong(), io.nextLong());
			double[] ti = new double[m];
			for(int i=0;i<m;i++) {
				ti[i] = (double) tb[i] / tx[i].subtract(ex).normSq();
			}
			boolean[][] block = new boolean[m][n];
			for(int i=0;i<n;i++) {
				Vector3.Long oa = ex.subtract(sx[i]);
				for(int j=0;j<m;j++) {
					block[j][i] = Vector3.Long.sphericalShellAndSegmentIntersects(oa, tx[j].subtract(sx[i]), sr[i]);
				}
			}
			double max = 0;
			LOOP: for(int i=1;i<(1<<m);i++) {
				double sum = 0;
				for(int j=0;j<m;j++) {
					if ((i&(1<<j)) > 0) {
						sum += ti[j];
					}
				}
				if (sum <= max) {
					continue;
				}
				int count = 0;
				boolean[] b = new boolean[n];
				for(int j=0;j<m;j++) {
					if ((i&(1<<j)) > 0) {
						for(int k=0;k<n;k++) {
							if (!b[k] && block[j][k]) {
								count++;
								b[k] = true;
								if (count > r) {
									continue LOOP;
								}
							}
						}
					}
				}
				max = sum;
			}
			io.println(max);
		}
		io.flush();
	}

}
abstract class Vector3 {
	public static class Long extends Vector3 {
		public static final Vector3.Long ZERO = new Vector3.Long(0, 0, 0);
		public long x;
		public long y;
		public long z;
		public Long() {
		}
		public Long(long x,long y,long z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
		public long dot(Long v) {
			return x * v.x + y * v.y + z * v.z;
		}
		public Long cross(Long v) {
			return new Long(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x); 
		}
		public Long add(Long v) {
			return new Long(x + v.x, y + v.y, z + v.z);
		}
		public Long subtract(Long v) {
			return new Long(x - v.x, y - v.y, z - v.z);
		}
		public Long multiply(long k) {
			return new Long(k * x, k * y, k * z);
		}
		public long normSq() {
			return x * x + y * y + z * z;
		}
		public double norm() {
			return Math.sqrt(normSq());
		}
		public boolean isZero() {
			return x == 0 && y == 0 && z == 0;
		}
		public boolean equals(Object o) {
			if (o instanceof Vector3.Long) {
				Vector3.Long v = (Vector3.Long) o;
				return x == v.x && y == v.y && z == v.z;
			}
			return super.equals(o);
		}
		public String toString() {
			return "[" + this.x + "," + this.y + "]";
		}
		
		public static boolean sphericalShellAndSegmentIntersects(Long oa,Long ob,long r) {
			long aNormSq = oa.normSq();
			long bNormSq = ob.normSq();
			long rSq = r * r;
			if (aNormSq < rSq && bNormSq < rSq) {
				return false;
			}else if (aNormSq <= rSq || bNormSq <= rSq) {
				return true;
			}
			Long ab = ob.subtract(oa);
			if (ab.dot(oa) * ab.dot(ob) >= 0) {
				return false;
			}
			return (ab.cross(oa).normSq() <= r * r * ab.normSq());
		}
	}
}
class IO {
	BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
	StringBuilder out = new StringBuilder();
	int index = 0;
	String bfl = null;
	String[] bf = new String[0];
	private boolean read() {
		try {
			bfl = bi.readLine();
			if (bfl == null) {
				return false;
			}
			bf = bfl.split("\\s");
			index = 0;
		} catch (IOException e) {
			e.printStackTrace();
		}
		return true;
	}
	public boolean hasNext() { return index < bf.length ? true : read(); }
	public boolean hasNextLine() { return read(); }
	public String next() { return hasNext() ? bf[index++] : null; }
	public String nextLine() { return hasNextLine() ? bfl : null; }
	public int nextInt() { return Integer.parseInt(next()); }
	public long nextLong() { return Long.parseLong(next()); }
	public double nextDouble() { return Double.parseDouble(next()); };
	public void println(long x) { out.append(x); out.append("\n"); }
	public void println(double x) { out.append(x); out.append("\n"); }
	public void println(String s) { out.append(s); out.append("\n"); }
	public void print(long x) { out.append(x); }
	public void print(double x) { out.append(x); }
	public void print(String s) { out.append(s); }
	public void flush() {System.out.print(out); out = new StringBuilder(); }
	public int[] arrayInt(int n) {
		int[] a = new int[n];
		for(int i=0;i<n;i++) {
			a[i] = nextInt();
		}
		return a;
	}
	public long[] arrayLong(int n) {
		long[] a = new long[n];
		for(int i=0;i<n;i++) {
			a[i] = nextLong();
		}
		return a;
	}
	public double[] arrayDouble(int n) {
		double[] a = new double[n];
		for(int i=0;i<n;i++) {
			a[i] = nextDouble();
		}
		return a;
	}
}