/**
 * 
 */
package hu.herba.codejam;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;

/**
 * Base functionality, helper functions for CodeJam problem solver utilities.
 * 
 * @author csorbazoli
 */
public abstract class AbstractCodeJamBase {
    private static final String EXT_OUT = ".out";
    protected static final int STREAM_TYPE = 0;
    protected static final int FILE_TYPE = 1;
    protected static final int READER_TYPE = 2;
    private static final String DEFAULT_INPUT = "test_input";
    private static final String DEFAULT_OUTPUT = "test_output";

    private final File inputFolder;
    private final File outputFolder;

    public AbstractCodeJamBase(String[] args, int type) {
	String inputFolderName = AbstractCodeJamBase.DEFAULT_INPUT;
	String outputFolderName = AbstractCodeJamBase.DEFAULT_OUTPUT;
	if (args.length > 0) {
	    inputFolderName = args[0];
	}
	this.inputFolder = new File(inputFolderName);
	if (!this.inputFolder.exists()) {
	    this.showUsage("Input folder '" + this.inputFolder.getAbsolutePath() + "' not exists!");
	}
	if (args.length > 1) {
	    outputFolderName = args[1];
	}
	this.outputFolder = new File(outputFolderName);
	if (this.outputFolder.exists() && !this.outputFolder.canWrite()) {
	    this.showUsage("Output folder '" + this.outputFolder.getAbsolutePath() + "' not writeable!");
	} else if (!this.outputFolder.exists() && !this.outputFolder.mkdirs()) {
	    this.showUsage("Could not create output folder '" + this.outputFolder.getAbsolutePath() + "'!");
	}
	File[] inputFiles = this.inputFolder.listFiles();
	for (File inputFile : inputFiles) {
	    this.processInputFile(inputFile, type);
	}
    }

    /**
     * @return the inputFolder
     */
    public File getInputFolder() {
	return this.inputFolder;
    }

    /**
     * @return the outputFolder
     */
    public File getOutputFolder() {
	return this.outputFolder;
    }

    /**
     * @param input
     *            input reader
     * @param output
     *            output writer
     * @throws IOException
     *             in case input or output fails
     * @throws IllegalArgumentException
     *             in case the given input is invalid
     */
    @SuppressWarnings("unused")
    protected void process(BufferedReader reader, PrintWriter pw) throws IOException, IllegalArgumentException {
	System.out.println("NEED TO IMPLEMENT (reader/writer)!!!");
	System.exit(-2);
    }

    /**
     * @param input
     *            input file
     * @param output
     *            output file (will be overwritten)
     * @throws IOException
     *             in case input or output fails
     * @throws IllegalArgumentException
     *             in case the given input is invalid
     */
    protected void process(File input, File output) throws IOException, IllegalArgumentException {
	System.out.println("NEED TO IMPLEMENT (file/file)!!!");
	System.exit(-2);
    }

    /**
     * @param input
     *            input stream
     * @param output
     *            output stream
     * @throws IOException
     *             in case input or output fails
     * @throws IllegalArgumentException
     *             in case the given input is invalid
     */
    protected void process(InputStream input, OutputStream output) throws IOException, IllegalArgumentException {
	System.out.println("NEED TO IMPLEMENT (stream/stream)!!!");
	System.exit(-2);
    }

    /**
     * @param type
     * @param input
     * @param output
     */
    private void processInputFile(File input, int type) {
	long starttime = System.currentTimeMillis();
	System.out.println("Processing '" + input.getAbsolutePath() + "'...");
	File output = new File(this.outputFolder, input.getName() + AbstractCodeJamBase.EXT_OUT);
	if (type == AbstractCodeJamBase.STREAM_TYPE) {
	    InputStream is = null;
	    OutputStream os = null;
	    try {
		is = new FileInputStream(input);
		os = new FileOutputStream(output);
		this.process(is, os);
	    } catch (FileNotFoundException e) {
		this.showUsage("FileNotFound: " + e.getLocalizedMessage());
	    } catch (IllegalArgumentException excIA) {
		this.showUsage(excIA.getLocalizedMessage());
	    } catch (Exception exc) {
		System.out.println("Program failed: " + exc.getLocalizedMessage());
		exc.printStackTrace(System.out);
	    } finally {
		if (is != null) {
		    try {
			is.close();
		    } catch (IOException e) {
			System.out.println("Failed to close input: " + e.getLocalizedMessage());
		    }
		}
		if (os != null) {
		    try {
			os.close();
		    } catch (IOException e) {
			System.out.println("Failed to close output: " + e.getLocalizedMessage());
		    }
		}
	    }
	} else if (type == AbstractCodeJamBase.READER_TYPE) {
	    BufferedReader reader = null;
	    PrintWriter pw = null;
	    try {
		reader = new BufferedReader(new FileReader(input));
		pw = new PrintWriter(output);
		this.process(reader, pw);
	    } catch (FileNotFoundException e) {
		this.showUsage("FileNotFound: " + e.getLocalizedMessage());
	    } catch (IllegalArgumentException excIA) {
		this.showUsage(excIA.getLocalizedMessage());
	    } catch (Exception exc) {
		System.out.println("Program failed: " + exc.getLocalizedMessage());
		exc.printStackTrace(System.out);
	    } finally {
		if (reader != null) {
		    try {
			reader.close();
		    } catch (IOException e) {
			System.out.println("Failed to close input: " + e.getLocalizedMessage());
		    }
		}
		if (pw != null) {
		    pw.close();
		}
	    }
	} else if (type == AbstractCodeJamBase.FILE_TYPE) {
	    try {
		this.process(input, output);
	    } catch (IllegalArgumentException excIA) {
		this.showUsage(excIA.getLocalizedMessage());
	    } catch (Exception exc) {
		System.out.println("Program failed: " + exc.getLocalizedMessage());
		exc.printStackTrace(System.out);
	    }
	} else {
	    this.showUsage("Unknown type given: " + type + " (accepted values: 0,1)");
	}
	System.out.println("  READY (" + (System.currentTimeMillis() - starttime) + " ms)");
    }

    /**
     * Read a single number from input
     * 
     * @param reader
     * @param purpose
     *            What is the purpose of given data
     * @return
     * @throws IOException
     * @throws IllegalArgumentException
     */
    protected int readInt(BufferedReader reader, String purpose) throws IOException, IllegalArgumentException {
	int ret = 0;
	String line = reader.readLine();
	if (line == null) {
	    throw new IllegalArgumentException("Invalid input: line is empty, it should be an integer (" + purpose + ")!");
	}
	try {
	    ret = Integer.parseInt(line);
	} catch (NumberFormatException excNF) {
	    throw new IllegalArgumentException("Invalid input: the first line '" + line + "' should be an integer (" + purpose + ")!");
	}
	return ret;
    }

    /**
     * Read array of integers
     * 
     * @param reader
     * @param purpose
     * @return
     */
    protected int[] readIntArray(BufferedReader reader, String purpose) throws IOException {
	int[] ret = null;
	String line = reader.readLine();
	if (line == null) {
	    throw new IllegalArgumentException("Invalid input: line is empty, it should be an integer list (" + purpose + ")!");
	}
	String[] strArr = line.split("\\s");
	int len = strArr.length;
	ret = new int[len];
	for (int i = 0; i < len; i++) {
	    try {
		ret[i] = Integer.parseInt(strArr[i]);
	    } catch (NumberFormatException excNF) {
		throw new IllegalArgumentException("Invalid input: line '" + line + "' should be an integer list (" + purpose + ")!");
	    }
	}
	return ret;
    }

    /**
     * Read array of strings
     * 
     * @param reader
     * @param purpose
     * @return
     */
    protected String[] readStringArray(BufferedReader reader, String purpose) throws IOException {
	String[] ret = null;
	String line = reader.readLine();
	if (line == null) {
	    throw new IllegalArgumentException("Invalid input: line is empty, it should be a string list (" + purpose + ")!");
	}
	ret = line.split("\\s");
	return ret == null ? new String[0] : ret;
    }

    /**
     * Basic usage pattern. Can be overwritten by current implementation
     * 
     * @param message
     *            Short message, describing the problem with given program
     *            arguments
     */
    protected void showUsage(String message) {
	if (message != null) {
	    System.out.println(message);
	}
	System.out.println("Usage:");
	System.out.println("\t" + this.getClass().getName() + " program");
	System.out.println("\tArguments:");
	System.out.println("\t\t<input folder>:\tpath of input folder (default: " + AbstractCodeJamBase.DEFAULT_INPUT + ").");
	System.out.println("\t\t               \tAll files will be processed in the folder");
	System.out.println("\t\t<output folder>:\tpath of output folder (default: " + AbstractCodeJamBase.DEFAULT_OUTPUT + ")");
	System.out.println("\t\t               \tOutput file name will be the same as input");
	System.out.println("\t\t               \tinput with extension '.out'");
	System.exit(-1);
    }
}

import java.io.*;
import java.util.*;

/**
 * @author: Ignat Alexeyenko
 * Date: 4/14/12
 */
public class DancingWithGooglersMain {

    public static final int MAX_LENGTH = 1024;

    public static void main(String[] args) {
        DancingWithGooglersMain main = new DancingWithGooglersMain();
        main.runConsoleApp(System.in, System.out);
    }

    public void runConsoleApp(InputStream inputStream, OutputStream outputStream) {
        final String s = readLn(inputStream, MAX_LENGTH);
        Integer cases = Integer.valueOf(s);
        Writer writer = new OutputStreamWriter(outputStream);
        for (int i= 0; i < cases; i++) {
            String rawLine = readLn(inputStream, MAX_LENGTH);

            try {
                writer.write("Case #" + (i + 1) + ": " + runFunction(rawLine) + "\n");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        try {
            writer.flush();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    private long runFunction(String rawLine) {
        String[] edgesArr = rawLine.split(" ");

        int numOfGooglers = Integer.valueOf(edgesArr[0]);
        int surprises = Integer.valueOf(edgesArr[1]);
        int minScoreP = Integer.valueOf(edgesArr[2]);

        List<Integer> marksT = new ArrayList<Integer>(numOfGooglers);
        for (int t = 0; t < numOfGooglers; t++) {
            marksT.add(Integer.valueOf(edgesArr[t + 3]));
        }

        return caclulateAmountOfGooglersThatExceedScoreP(surprises, minScoreP, marksT);
    }

    private int caclulateAmountOfGooglersThatExceedScoreP(int surprises, int minScoreP, List<Integer> marksT) {
        Map<Integer, Set<Mark>> sumToPermutations = new HashMap<Integer, Set<Mark>>(marksT.size());

        for (Integer theSum : marksT) {
            Set<Mark> allPossiblePermutations = getAllPossiblePermutations(theSum, minScoreP);
            sumToPermutations.put(theSum, allPossiblePermutations);
        }

        int exceedsWithoutSurprises = 0;
        int exceedsOnlyWithSurprises = 0;
        for (Integer theSum : marksT) {
            Set<Mark> marksPermutations = sumToPermutations.get(theSum);
            
            boolean exceeded = false;
            boolean needSurprise = true;
            for (Mark marksPermutation : marksPermutations) {
                if (marksPermutation.exceedsScore) {
                    exceeded = true;
                    if (!marksPermutation.surprise && needSurprise) {
                        needSurprise = false;
                    }
                }
            }
            
            if (exceeded && needSurprise) {
                exceedsOnlyWithSurprises++;
            }
            if (exceeded && !needSurprise) {
                exceedsWithoutSurprises++;
            }
        }

        return exceedsWithoutSurprises + Math.min(exceedsOnlyWithSurprises, surprises);
    }

    Set<Mark> getAllPossiblePermutations(int sum, int minScoreP) {
        Set<Mark> markList = new LinkedHashSet<Mark>(5);
        final int start = Math.max(sum / 3 - 2, 0);
        final int stop = sum / 3 + 2;
        for (int i = start; i <= stop; i++) {
            for (int j = start; j <= stop; j++) {
                for (int k = start; k <= stop; k++) {
                    final int divergence = Math.abs(max(i, j, k) - min(i, j, k));
                    if ((i + j + k == sum) && divergence <= 2) {
                        boolean exceedsScore = i >= minScoreP || j >= minScoreP || k >= minScoreP;
                        markList.add(new Mark(i, j, k, divergence == 2, exceedsScore));
                    }
                }
            }
        }
        return markList;
    }

    private static int min(int a, int b, int c) {
        return Math.min(Math.min(a, b), c);
    }

    private static int max(int a, int b, int c) {
        return Math.max(Math.max(a, b), c);
    }


    private String readLn(InputStream inputStream, int maxLength) {  // utility function to read from stdin,
        // Provided by Programming-challenges, edit for style only
        byte line[] = new byte[maxLength];
        int length = 0;
        int input = -1;
        try {
            while (length < maxLength) {//Read untill maxlength
                input = inputStream.read();
                if ((input < 0) || (input == '\n')) break; //or untill end of line ninput
                line[length++] += input;
            }

            if ((input < 0) && (length == 0)) return null;  // eof
            return new String(line, 0, length);
        } catch (IOException e) {
            return null;
        }
    }

    static class Mark {
        // array represents marks, always are sorted
        private List<Integer> marks;

        private boolean surprise;
        private boolean exceedsScore;

        Mark(int m0, int m1, int m2, boolean surprise, boolean exceedsScore) {
            this.marks = new ArrayList<Integer>(3);
            this.marks.add(m1);
            this.marks.add(m0);
            this.marks.add(m2);
            this.surprise = surprise;
            this.exceedsScore = exceedsScore;
            // todo: possibly just put elements in the list in a right order
            Collections.sort(this.marks);
            Collections.reverse(this.marks);
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Mark mark = (Mark) o;

            if (exceedsScore != mark.exceedsScore) return false;
            if (surprise != mark.surprise) return false;
            if (marks != null ? !marks.equals(mark.marks) : mark.marks != null) return false;

            return true;
        }

        @Override
        public int hashCode() {
            int result = marks != null ? marks.hashCode() : 0;
            result = 31 * result + (surprise ? 1 : 0);
            result = 31 * result + (exceedsScore ? 1 : 0);
            return result;
        }

        @Override
        public String toString() {
            return "Mark{" +
                    "marks=" + marks +
                    ", surprise=" + surprise +
                    ", exceedsScore=" + exceedsScore +
                    '}';
        }
    }
}
