Problem: Daniel is organizing a football tournament. He has come up with the following tournament format: 

  1. In the first several (possibly zero) stages, while the number of teams is even, they split in pairs and play one game for each pair. At each stage the loser of each pair is eliminated (there are no draws). Such stages are held while the number of teams is even. 
  2. Eventually there will be an odd number of teams remaining. If there is one team remaining, it will be declared the winner, and the tournament ends. Otherwise each of the remaining teams will play with each other remaining team once in round robin tournament (if there are x teams, there will be <image> games), and the tournament ends. 



For example, if there were 20 teams initially, they would begin by playing 10 games. So, 10 teams would be eliminated, and the remaining 10 would play 5 games. Then the remaining 5 teams would play 10 games in a round robin tournament. In total there would be 10+5+10=25 games.

Daniel has already booked the stadium for n games. Help him to determine how many teams he should invite so that the tournament needs exactly n games. You should print all possible numbers of teams that will yield exactly n games in ascending order, or -1 if there are no such numbers.

Input

The first line contains a single integer n (1 ≤ n ≤ 1018), the number of games that should be played.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print all possible numbers of invited teams in ascending order, one per line. If exactly n games cannot be played, output one number: -1.

Examples

Input

3


Output

3
4


Input

25


Output

20


Input

2


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

final public class Main implements Runnable {
	private static boolean local;

	public static void main(String[] args) {
		if (args.length > 0 && args[0].equals("-1")) {
			local = true;
		}
		new Thread(null, new Main(), "mainthread", 1 << 27).start();
	}

	public void run() {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;

		try {
			if (local) {
				inputStream = new FileInputStream("/home/outside/coding/workspace/java/main/io/input.txt");
				outputStream = new FileOutputStream("/home/outside/coding/workspace/java/main/io/output.txt");
			} else {
				// inputStream = new FileInputStream("input.txt");
				// outputStream = new FileOutputStream("output.txt");
			}
		} catch (Exception e) {
			throw new RuntimeException(e);
		}

		Task.in = new InputReader(inputStream);
		Task.out = new OutputWriter(outputStream);
		if (local) {
			Task.dout = new DebugWriter(Task.out);
		}
		new Task().solve();
		Task.out.close();
	}
}

final class Task {
	public static InputReader in;
	public static OutputWriter out;
	public static DebugWriter dout;

	public void solve() {
		long n = in.readLong();
		
		ArrayList<BigInteger> ans = new ArrayList<>();
		
		for (int p = 0; p < 100; ++p) {
			BigInteger x = BigInteger.valueOf(1);
			for (int i = 0; i < p; ++i)
				x = x.multiply(BigInteger.valueOf(2));
			
			
			BigInteger d = x.multiply(BigInteger.valueOf(2)).subtract(BigInteger.valueOf(3));
			d = d.multiply(d).add(BigInteger.valueOf(n).multiply(BigInteger.valueOf(8)));
			
			// dout.printLine(x + " " + d);
			
			if (sqrt(d) != BigInteger.valueOf(-1)) {
				BigInteger k = BigInteger.valueOf(3).subtract(x.multiply(BigInteger.valueOf(2))).add(sqrt(d));
				if (k.remainder(BigInteger.valueOf(2)).equals(BigInteger.ZERO) &&
					k.compareTo(BigInteger.ZERO) > 0 &&
					!k.divide(BigInteger.valueOf(2)).remainder(BigInteger.valueOf(2)).equals(BigInteger.ZERO))
					ans.add(k.divide(BigInteger.valueOf(2)).multiply(x));
				
				k = BigInteger.valueOf(3).subtract(x.multiply(BigInteger.valueOf(2))).subtract(sqrt(d));
				if (k.remainder(BigInteger.valueOf(2)).equals(BigInteger.ZERO) &&
					k.compareTo(BigInteger.ZERO) > 0 &&
					!k.divide(BigInteger.valueOf(2)).remainder(BigInteger.valueOf(2)).equals(BigInteger.ZERO))
					ans.add(k.divide(BigInteger.valueOf(2)).multiply(x));
			}
			
			// dout.printLine(ans);
		}
		
		
		
		if (ans.size() == 0) out.printLine(-1);
		else {
			SequenceUtils.quickSort(ans);
			// ans = SequenceUtils.unique(ans);
			for (int i = 0; i < ans.size(); ++i)
				out.printLine(ans.get(i));
		}
		
	}
	
	BigInteger sqrt(BigInteger n) {
		BigInteger lo = BigInteger.valueOf(1);
		BigInteger hi = n;
		while (lo.compareTo(hi) < 0) {
			BigInteger m = lo.add(hi.subtract(lo).divide(BigInteger.valueOf(2)));
			if (m.multiply(m).compareTo(n) < 0) lo = m.add(BigInteger.valueOf(1));
			else hi = m;
		}
		
		if (lo.multiply(lo).equals(n)) return lo;
		return BigInteger.valueOf(-1);
	}
}

final class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1 << 13];
	private int curChar;
	private int numChars;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	private int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int peek() {
		if (numChars == -1)
			return -1;
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				return -1;
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long readLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public String readString() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public static boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private String readLine0() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != '\n' && c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public String readLine() {
		String s = readLine0();
		while (s.trim().length() == 0)
			s = readLine0();
		return s;
	}

	public String readLine(boolean ignoreEmptyLines) {
		if (ignoreEmptyLines)
			return readLine();
		else
			return readLine0();
	}
	
	public String readToEnd() {
		StringBuilder buf = new StringBuilder();
		int c = read();
		while (c != -1) {
			if (c != '\r')
				buf.appendCodePoint(c);
			c = read();
		}
		return buf.toString();
	}

	public BigInteger readBigInteger() {
		try {
			return new BigInteger(readString());
		} catch (NumberFormatException e) {
			throw new InputMismatchException();
		}
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public double readDouble() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		}
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
			}
		}
		return res * sgn;
	}

	public boolean isExhausted() {
		int value;
		while (isSpaceChar(value = peek()) && value != -1)
			read();
		return value == -1;
	}
	
	public void close() {
		try {
			stream.close();
		} catch (IOException e) {
			throw new RuntimeException();			
		}
	}
}

final class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream), 1 << 13));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}


	public void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object... objects) {
		print(objects);
		writer.println();
	}

	public void printFormat(String format, Object... objects) {
		writer.printf(format, objects);
	}


	public void print(char[] objects) {
		writer.print(objects);
	}

	public void printLine(char[] objects) {
		writer.println(objects);
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(int[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(int[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(short[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(short[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(long[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(long[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(double[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(double[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(byte[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(byte[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void print(boolean[] objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(boolean[] objects) {
		print(objects);
		writer.println();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
	}


	public void close() {
		writer.close();
	}

	public void flush() {
		writer.flush();
	}
}

final class DebugWriter {
	private final OutputWriter writer;

	public DebugWriter(OutputWriter writer) {
		this.writer = writer;
	}

	private void printDebugMessage() {
		writer.print("DEBUG:\t");
	}

	public void printLine(Object... objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printFormat(String format, Object... objects) {
		printDebugMessage();
		writer.printFormat(format, objects);
		flush();
	}

	public void printLine(char[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(char[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(double[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(double[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(int[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(int[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(short[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(short[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(long[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(long[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(byte[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(byte[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void printLine(boolean[] objects) {
		printDebugMessage();
		writer.printLine(objects);
		flush();
	}

	public void printLine(boolean[][] objects) {
		for (int i = 0; i < objects.length; ++i)
			printLine(objects[i]);
		flush();
	}

	public void flush() {
		writer.flush();
	}
}


final class SequenceUtils {
	// swap
	public final static <T> void swap(List<T> sequence, int j, int i) {
		T tmp = sequence.get(j);
		sequence.set(j, sequence.get(i));
		sequence.set(i, tmp);
	}

	public final static <T> void swap(T[] sequence, int j, int i) {
		T tmp = sequence[j];
		sequence[j] = sequence[i];
		sequence[i] = tmp;
	}

	public final static void swap(int[] sequence, int j, int i) {
		int tmp = sequence[j];
		sequence[j] = sequence[i];
		sequence[i] = tmp;
	}

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

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

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

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

	public final static void swap(short[] sequence, int j, int i) {
		short tmp = sequence[j];
		sequence[j] = sequence[i];
		sequence[i] = tmp;
	}

	public final static void swap(byte[] sequence, int j, int i) {
		byte tmp = sequence[j];
		sequence[j] = sequence[i];
		sequence[i] = tmp;
	}

	// reverse
	public final static <T> void reverse(List<T> sequence) {
		for (int left = 0, right = sequence.size() - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static <T> void reverse(T[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(int[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(long[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(char[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(double[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(boolean[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(short[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	public final static void reverse(byte[] sequence) {
		for (int left = 0, right = sequence.length - 1; left < right; ++left, --right)
			swap(sequence, left, right);
	}

	// next permutation
	public final static <T extends Comparable<T>> boolean nextPermutation(List<T> sequence) {
		for (int j = sequence.size() - 2; j >= 0; --j) {
			if (sequence.get(j).compareTo(sequence.get(j + 1)) < 0) {
				reverse(sequence.subList(j + 1, sequence.size()));
				for (int i = j + 1; i < sequence.size(); ++i)
					if (sequence.get(j).compareTo(sequence.get(i)) < 0) {
						swap(sequence, j, i);
						return true;
					}
			}
		}
		return false;
	}

	public final static <T> boolean nextPermutation(List<T> sequence, Comparator<T> comparator) {
		for (int j = sequence.size() - 2; j >= 0; --j) {
			if (comparator.compare(sequence.get(j), sequence.get(j + 1)) < 0) {
				reverse(sequence.subList(j + 1, sequence.size()));
				for (int i = j + 1; i < sequence.size(); ++i)
					if (comparator.compare(sequence.get(j), sequence.get(i)) < 0) {
						swap(sequence, j, i);
						return true;
					}
			}
		}
		return false;
	}

	// random shuffle
	public final static <T> void shuffle(List<T> sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.size(); ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static <T> void shuffle(T[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(int[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(long[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(char[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(double[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(boolean[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(short[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	public final static void shuffle(byte[] sequence) {
		Random random = new Random(System.nanoTime());
		for (int i = 1; i < sequence.length; ++i)
			swap(sequence, random.nextInt(i + 1), i);
	}

	// merge sort
	public final static <T extends Comparable<T>> void mergeSort(List<T> sequence) {
		int n = sequence.size();
		T[] tmp = (T[]) new Object[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence.get(i);
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static <T extends Comparable<T>> void merge(List<T> sequence, T[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence.set(i, tmp[pRight++]);
			else if (pRight > right) sequence.set(i, tmp[pLeft++]);
			else if (tmp[pLeft].compareTo(tmp[pRight]) <= 0) sequence.set(i, tmp[pLeft++]);
			else sequence.set(i, tmp[pRight++]);
	}


	public final static <T extends Comparable<T>> void mergeSort(T[] sequence) {
		int n = sequence.length;
		T[] tmp = (T[]) new Object[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static <T extends Comparable<T>> void merge(T[] sequence, T[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft].compareTo(tmp[pRight]) <= 0) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static <T> void mergeSort(List<T> sequence, Comparator<T> comparator) {
		int n = sequence.size();
		T[] tmp = (T[]) new Object[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence.get(i);
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1), comparator);
		}
	}

	private final static <T> void merge(List<T> sequence, T[] tmp, int left, int mid, int right, Comparator<T> comparator) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence.set(i, tmp[pRight++]);
			else if (pRight > right) sequence.set(i, tmp[pLeft++]);
			else if (comparator.compare(tmp[pLeft], tmp[pRight]) <= 0) sequence.set(i, tmp[pLeft++]);
			else sequence.set(i, tmp[pRight++]);
	}


	public final static <T> void mergeSort(T[] sequence, Comparator<T> comparator) {
		int n = sequence.length;
		T[] tmp = (T[]) new Object[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1), comparator);
		}
	}

	private final static <T> void merge(T[] sequence, T[] tmp, int left, int mid, int right, Comparator<T> comparator) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (comparator.compare(tmp[pLeft], tmp[pRight]) <= 0) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(int[] sequence) {
		int n = sequence.length;
		int[] tmp = new int[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(int[] sequence, int[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(long[] sequence) {
		int n = sequence.length;
		long[] tmp = new long[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(long[] sequence, long[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(char[] sequence) {
		int n = sequence.length;
		char[] tmp = new char[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(char[] sequence, char[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(double[] sequence) {
		int n = sequence.length;
		double[] tmp = new double[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(double[] sequence, double[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(boolean[] sequence) {
		int n = sequence.length;
		boolean[] tmp = new boolean[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(boolean[] sequence, boolean[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (!tmp[pLeft] || tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(short[] sequence) {
		int n = sequence.length;
		short[] tmp = new short[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(short[] sequence, short[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}


	public final static void mergeSort(byte[] sequence) {
		int n = sequence.length;
		byte[] tmp = new byte[n];
		for (int step = 1; step < n; step *= 2) {
			for (int i = 0; i < n; ++i)
				tmp[i] = sequence[i];
			for (int i = 0; i + step < n; i += 2 * step)
				merge(sequence, tmp, i, i + step - 1, Math.min(i + step * 2 - 1, n - 1));
		}
	}

	private final static void merge(byte[] sequence, byte[] tmp, int left, int mid, int right) {
		int pLeft = left;
		int pRight = mid + 1;
		for (int i = left; i <= right; ++i)
			if (pLeft > mid) sequence[i] = tmp[pRight++];
			else if (pRight > right) sequence[i] = tmp[pLeft++];
			else if (tmp[pLeft] <= tmp[pRight]) sequence[i] = tmp[pLeft++];
			else sequence[i] = tmp[pRight++];
	}

	// quick sort
	public final static <T extends Comparable<T>> void quickSort(List<T> sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.size() - 1);
	}

	private final static <T extends Comparable<T>> void quickSortImplementation(List<T> sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		T value = sequence.get(left);

		while (i <= greaterThen) {
			int cmp = sequence.get(i).compareTo(value);
			if (cmp < 0) swap(sequence, i++, lessThen++);
			else if (cmp > 0) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static <T extends Comparable<T>> void quickSort(T[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static <T extends Comparable<T>> void quickSortImplementation(T[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		T value = sequence[left];

		while (i <= greaterThen) {
			int cmp = sequence[i].compareTo(value);
			if (cmp < 0) swap(sequence, i++, lessThen++);
			else if (cmp > 0) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static <T> void quickSort(List<T> sequence, Comparator<T> comparator) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.size() - 1, comparator);
	}

	private final static <T> void quickSortImplementation(List<T> sequence, int left, int right, Comparator<T> comparator) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		T value = sequence.get(left);

		while (i <= greaterThen) {
			int cmp = comparator.compare(sequence.get(i), value);
			if (cmp < 0) swap(sequence, i++, lessThen++);
			else if (cmp > 0) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1, comparator);
		quickSortImplementation(sequence, greaterThen + 1, right, comparator);
	}


	public final static <T> void quickSort(T[] sequence, Comparator<T> comparator) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1, comparator);
	}

	private final static <T> void quickSortImplementation(T[] sequence, int left, int right, Comparator<T> comparator) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		T value = sequence[left];

		while (i <= greaterThen) {
			int cmp = comparator.compare(sequence[i], value);
			if (cmp < 0) swap(sequence, i++, lessThen++);
			else if (cmp > 0) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1, comparator);
		quickSortImplementation(sequence, greaterThen + 1, right, comparator);
	}


	public final static void quickSort(int[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(int[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		int value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(long[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(long[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		long value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(char[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(char[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		char value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(double[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(double[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		double value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(boolean[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(boolean[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		boolean value = sequence[left];

		while (i <= greaterThen) {
			if (!sequence[i] && value) swap(sequence, i++, lessThen++);
			else if (sequence[i] && !value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(short[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(short[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		short value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}


	public final static void quickSort(byte[] sequence) {
		shuffle(sequence);
		quickSortImplementation(sequence, 0, sequence.length - 1);
	}

	private final static void quickSortImplementation(byte[] sequence, int left, int right) {
		if (left >= right) return;

		int lessThen = left;
		int greaterThen = right;
		int i = left;
		byte value = sequence[left];

		while (i <= greaterThen) {
			if (sequence[i] < value) swap(sequence, i++, lessThen++);
			else if (sequence[i] > value) swap(sequence, i, greaterThen--);
			else ++i;
		}

		quickSortImplementation(sequence, left, lessThen - 1);
		quickSortImplementation(sequence, greaterThen + 1, right);
	}

	// unique
	public static <T> ArrayList<T> unique(ArrayList<T> sequence) {
		int size = 1;
		for (int i = 1; i < sequence.size(); ++i)
			if (!sequence.get(i).equals(sequence.get(i - 1)))
				++size;

		ArrayList<T> newSequence = new ArrayList<T>(size);
		newSequence.add(sequence.get(0));

		for (int i = 1; i < sequence.size(); ++i)
			if (!sequence.get(i).equals(sequence.get(i - 1)))
				newSequence.add(sequence.get(i));

		return newSequence;
	}

	public static <T> T[] unique(T[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (!sequence[i].equals(sequence[i - 1]))
				++size;

		T[] newSequence = (T[]) new Object[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (!sequence[i].equals(sequence[i - 1]))
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static int[] unique(int[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		int[] newSequence = new int[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static long[] unique(long[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		long[] newSequence = new long[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static char[] unique(char[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		char[] newSequence = new char[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static double[] unique(double[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		double[] newSequence = new double[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static boolean[] unique(boolean[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		boolean[] newSequence = new boolean[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static short[] unique(short[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		short[] newSequence = new short[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}

	public static byte[] unique(byte[] sequence) {
		int size = 1;
		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				++size;

		byte[] newSequence = new byte[size];
		newSequence[0] = sequence[0];
		size = 0;

		for (int i = 1; i < sequence.length; ++i)
			if (sequence[i] != sequence[i - 1])
				newSequence[++size] = sequence[i];

		return newSequence;
	}
}