/**
 * 
 */
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);
    }
}

package qualifiers12.b;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class Dancing {

    public static Set<Triple>[] combs;

    public static class Triple {
	protected final int total;
	protected final int v1;
	protected final int v2;
	protected final int v3;

	public Triple(int total, int v1, int v2, int v3) {
	    this.total = total;
	    this.v1 = v1;
	    this.v2 = v2;
	    this.v3 = v3;
	}

	public int getMax() {
	    return max2(max2(v1, v2), v3);
	}

	private int max2(int n1, int n2) {
	    return (n1 > n2) ? n1 : n2;
	}

	public int getTotal() {
	    return v1 + v2 + v3;
	}

	public boolean isTriplet() {
	    if (v1 < 0 || v2 < 0 || v3 < 0) {
		return false;
	    }
	    if (Math.abs(v1 - v2) > 2 || Math.abs(v1 - v3) > 2 || Math.abs(v2 - v3) > 2) {
		return false;
	    }
	    return v1 + v2 + v3 == total;
	}

	public boolean isSurprising() {
	    return Math.abs(v1 - v2) == 2 || Math.abs(v1 - v3) == 2 || Math.abs(v2 - v3) == 2;
	}

	@Override
	public String toString() {
	    return total + "(" + v1 + "," + v2 + "," + v3 + ")";
	}

	@Override
	public int hashCode() {
	    List<Integer> list = new ArrayList<Integer>();
	    list.add(v1);
	    list.add(v2);
	    list.add(v3);
	    Collections.sort(list);
	    return list.get(0) * 100 + list.get(1) * 10 + list.get(2);
	}

	@Override
	public boolean equals(Object obj) {
	    if (obj instanceof Triple) {
		Triple that = (Triple) obj;
		if ((this.v1 == that.v1 || this.v1 == that.v2 || this.v1 == that.v3)
			&& (this.v2 == that.v1 || this.v2 == that.v2 || this.v2 == that.v3)
			&& (this.v3 == that.v1 || this.v3 == that.v2 || this.v3 == that.v3)) {
		    return true;
		} else {
		    return false;
		}
	    } else {
		return false;
	    }
	}
    }

    public static void computeCombination(int k, int total) {
	int avgPart = Math.round((total + 0.0f) / 3.0f);
	for (int i = -1; i < 2; i++) {
	    computeCombinationGiven(k, total, avgPart + i);
	}
    }

    private static void computeCombinationGiven(int k, int total, int part) {
	int missing = total - part;
	int avgPart = Math.round((missing + 0.0f) / 2.0f);

	for (int i = -1; i < 2; i++) {
	    computeWithOne(k, total, part, avgPart + i, avgPart);
	}
    }

    private static void computeWithOne(int k, int total, int part1, int part2, int lastAvg) {
	for (int i = -1; i < 2; i++) {
	    Triple triple = new Triple(total, part1, part2, lastAvg + i);
	    if (triple.isTriplet()) {
		combs[k].add(triple);
	    }
	}
    }

    public static void main(String[] args) throws IOException {

	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	String s = in.readLine();

	int cases = Integer.parseInt(s);

	for (int i = 0; i < cases; i++) {
	    s = in.readLine();
	    StringTokenizer tokenizer = new StringTokenizer(s, " ");

	    int[] totals = new int[Integer.parseInt(tokenizer.nextToken())];
	    combs = new Set[totals.length];
	    for (int k = 0; k < combs.length; k++) {
		combs[k] = new HashSet<Triple>();
	    }
	    int surprising = Integer.parseInt(tokenizer.nextToken());
	    int p = Integer.parseInt(tokenizer.nextToken());

	    int k = 0;
	    while (tokenizer.hasMoreTokens()) {
		totals[k] = Integer.parseInt(tokenizer.nextToken());
		computeCombination(k, totals[k]);
		k++;
	    }

	    // for (k = 0; k < combs.length; k++) {
	    //
	    // String tmp = "";
	    // for (Triple triple : combs[k]) {
	    // tmp += triple.toString() + " ";
	    // }
	    // System.out.println(tmp);
	    //
	    // }

	    int usedSurprising = 0;
	    for (k = 0; k < combs.length; k++) {

		if (containsSurprisingSequence(combs[k])) {
		    Triple triple = containsNonSurprisingAboveOrEqualP(combs[k], p);
		    if (triple != null) {
			combs[k].clear();
			combs[k].add(triple);
		    } else if (usedSurprising < surprising) {
			triple = containsSurprisingAboveOrEqualP(combs[k], p);
			if (triple != null) {
			    combs[k].clear();
			    combs[k].add(triple);
			    usedSurprising++;
			}
		    } else {
			Iterator<Triple> iter = combs[k].iterator();
			while (iter.hasNext()) {
			    triple = iter.next();
			    if (triple.isSurprising()) {
				continue;
			    }
			    combs[k].clear();
			    combs[k].add(triple);
			    break;
			}
		    }
		} else {
		    // choose one above P, otherwise random one
		    Triple triple = containsNonSurprisingAboveOrEqualP(combs[k], p);
		    if (triple != null) {
			combs[k].clear();
			combs[k].add(triple);
		    } else {
			Iterator<Triple> iter = combs[k].iterator();
			while (iter.hasNext()) {
			    triple = iter.next();
			    if (triple.isSurprising()) {
				continue;
			    }
			    combs[k].clear();
			    combs[k].add(triple);
			    break;
			}
		    }
		}
	    }

	    int res = 0;
	    for (k = 0; k < combs.length; k++) {
		for (Triple triple : combs[k]) {
		    if (triple.getMax() >= p) {
			res++;
		    }
		}
	    }

	    String result = "Case #" + (i + 1) + ": " + res;
	    System.out.println(result);
	}

    }

    private static boolean containsSurprisingSequence(Set<Triple> triples) {
	for (Triple triple : triples) {
	    if (triple.isSurprising()) {
		return true;
	    }
	}
	return false;
    }

    private static Triple containsSurprisingAboveOrEqualP(Set<Triple> triples, int p) {
	for (Triple triple : triples) {
	    if (triple.isSurprising()) {
		if (triple.getMax() >= p) {
		    return triple;
		}
	    }
	}
	return null;
    }

    private static Triple containsNonSurprisingAboveOrEqualP(Set<Triple> triples, int p) {
	for (Triple triple : triples) {
	    if (!triple.isSurprising()) {
		if (triple.getMax() >= p) {
		    return triple;
		}
	    }
	}
	return null;
    }
}
