Problem: Everybody knows that the capital of Berland is connected to Bercouver (the Olympic capital) by a direct road. To improve the road's traffic capacity, there was placed just one traffic sign, limiting the maximum speed. Traffic signs in Berland are a bit peculiar, because they limit the speed only at that point on the road where they are placed. Right after passing the sign it is allowed to drive at any speed.

It is known that the car of an average Berland citizen has the acceleration (deceleration) speed of a km/h2, and has maximum speed of v km/h. The road has the length of l km, and the speed sign, limiting the speed to w km/h, is placed d km (1 ≤ d < l) away from the capital of Berland. The car has a zero speed at the beginning of the journey. Find the minimum time that an average Berland citizen will need to get from the capital to Bercouver, if he drives at the optimal speed.

The car can enter Bercouver at any speed.

Input

The first line of the input file contains two integer numbers a and v (1 ≤ a, v ≤ 10000). The second line contains three integer numbers l, d and w (2 ≤ l ≤ 10000; 1 ≤ d < l; 1 ≤ w ≤ 10000).

Output

Print the answer with at least five digits after the decimal point.

Examples

Input

1 1
2 1 3


Output

2.500000000000


Input

5 70
200 170 40


Output

8.965874696353

Solution (in JAVA):

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

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Task solver = new D();
		solver.solve(1, in, out);
		out.close();
	}
}

interface Task {
	public void solve(int testNumber, InputReader in, OutputWriter out);
}

class A implements Task {

	char[] arr;

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		int ret = 0, n = 0;
		while (true) {
			try {
				arr = in.readLine().toCharArray();
				if (arr[0] == '+')
					n++;
				else if (arr[0] == '-')
					n--;
				else
					for (int i = 0; i < arr.length; i++)
						if (arr[i] == ':') {
							ret += n * (arr.length - i - 1);
							// out.printLine(i, arr.length);
						}
			} catch (Exception ex) {
				break;
			}
		}
		out.printLine(ret);
	}
}

class B implements Task {

	ArrayList<String> lista = new ArrayList<String>();
	char[][] arr;

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		while (true) {
			try {
				lista.add(in.readLine(false));
				// out.printLine(lista.get(lista.size()-1));
			} catch (Exception ex) {
				break;
			}
		}
		lista.remove(lista.size()-1);
		int c = 0, max = 0;
		for (String str : lista) {
			max = MiscUtils.max(max, str.length());
			// out.printLine(str, str.length());
		}
		arr = new char[lista.size() + 2][max + 2];
		Arrays.fill(arr[0], '*');
		Arrays.fill(arr[arr.length - 1], '*');
		for (int i = 1; i < arr.length - 1; i++) {
			int n = max - lista.get(i - 1).length();
			arr[i][0] = arr[i][max + 1] = '*';
			if (n % 2 == 1) {
				for (int j = 1; j <= n / 2 + c; j++)
					arr[i][j] = ' ';
				for (int j = 1; j <= lista.get(i - 1).length(); j++)
					arr[i][n / 2 + c + j] = lista.get(i - 1).charAt(j - 1);
				for (int j = 0; j < n / 2 + 1 - c; j++)
					arr[i][max - j] = ' ';
				c = 1 - c;
			} else {
				for (int j = 1; j <= n / 2; j++)
					arr[i][j] = ' ';
				for (int j = 1; j <= lista.get(i - 1).length(); j++)
					arr[i][n / 2 + j] = lista.get(i - 1).charAt(j - 1);
				for (int j = 0; j < n / 2; j++)
					arr[i][max - j] = ' ';
			}
		}
		IOUtils.printTable(out, arr);
	}
}

class C implements Task {

	char[] arr;
	int[] counter;
	IntArrayList lista=new IntArrayList();
		
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		arr=in.readString().toCharArray();
		counter=new int[arr.length+1];
		for (int i=0; i<arr.length; i++) {
			if (arr[i]=='(') lista.add(i);
			else if (lista.size()>0) {
				counter[lista.popBack()]++;
				counter[i+1]--;
			}
		}
		int ret=0, c=0, q=1;
		for (int i=0; i<=arr.length; i++) {
			if (i>0) counter[i]+=counter[i-1];
			if (counter[i]>0) c++;
			else c=0;
			if (c>ret) {
				ret=c;
				q=1;
			}
			else if (c==ret) q++;
		}
		if (ret==0) q=1;
		out.printLine(ret, q);
	}

}

class D implements Task {

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		double a=in.readDouble(), v=in.readDouble(), l=in.readDouble(), d=in.readDouble(), w=in.readDouble();
		w=MiscUtils.min(w, v);
		double s1=0.5*v*v/a, s3=0.5*(v*v-w*w)/a, s2, t1, t2, t3, v0;
		if (0.5*w*w/a>d) {
			s1=d;
			s3=0.0;
			t3=0.0;
			v0=Math.sqrt(2.0*a*d);
		}
		else if (s1+s3>d) {
			s1=0.25*(2.0*a*d+w*w)/a;
			s3=0.25*(2.0*a*d-w*w)/a;
			t3=raiz(0.5*a, w, -s3);
			v0=w;
		}
		else {
			t3=raiz(0.5*a, w, -s3);
			v0=w;
		}
		s2=d-s1-s3;
		t1=Math.sqrt(2.0*s1/a);
		t2=s2/v;
		double s4=MiscUtils.min(0.5*(v*v-v0*v0)/a, l-d), s5=l-d-s4, t4=raiz(0.5*a, v0, -s4), t5=s5/v;
//		out.printLine(s1, t1, s2, t2, s3, t3, s4+s5, t4+t5);
		out.printLine(t1+t2+t3+t4+t5);
	}
	
	double raiz(double a, double b, double c) {
		return 0.5*(-b+Math.sqrt(b*b-4.0*a*c))/a;
	}

}

class E implements Task {

	int[] arr, memo;
	int n;

	public void solve(int testNumber, InputReader in, OutputWriter out) {
		n = in.readInt();
		int ret = 0;
		arr = IOUtils.readIntArray(in, n);
		memo = new int[1 << n];
		Arrays.fill(memo, -1);
		out.printLine(pd((1 << n) - 1));
	}

	int pd(int mask) {
		if (memo[mask] != -1)
			return memo[mask];
		if (mask == 0)
			return memo[0] = 0;
		memo[mask] = 1000000;
		int soma = 0;
		for (int i = 0; i < n; i++)
			if ((mask & (1 << i)) > 0)
				soma += arr[i];
		for (int i = 0; i < n; i++)
			if ((mask & (1 << i)) > 0) {
				int mask2 = mask, c = 0;
				for (int j = 0; j < 3; j++) {
					int k = (i + j) % n;
					if ((mask & (1 << k)) > 0) {
						c += arr[k];
						mask2 ^= 1 << k;
					}
				}
				memo[mask] = MiscUtils.min(memo[mask], soma - c + pd(mask2));
			}
		return memo[mask];
	}

}

class InputReader {
	private boolean finished = false;

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

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

	public 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 {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(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 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 String next() {
		return readString();
	}

	public SpaceCharFilter getFilter() {
		return filter;
	}

	public void setFilter(SpaceCharFilter filter) {
		this.filter = filter;
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				outputStream)));
	}

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

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

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

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

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

	public void print(IntCollection collection) {
		boolean first = true;
		for (IntIterator iterator = collection.iterator(); iterator.isValid(); iterator
				.advance()) {
			if (first)
				first = false;
			else
				writer.print(' ');
			writer.print(iterator.value());
		}
	}

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

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

	public void printLine(IntCollection collection) {
		print(collection);
		writer.println();
	}

	public void printLine() {
		writer.println();
	}

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

	public void print(char i) {
		writer.print(i);
	}

	public void printLine(char i) {
		writer.println(i);
	}

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

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

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

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

	public void print(long i) {
		writer.print(i);
	}

	public void printLine(long i) {
		writer.println(i);
	}

	public void print(int i) {
		writer.print(i);
	}

	public void printLine(int i) {
		writer.println(i);
	}
}

class IOUtils {
	public static Pair<Integer, Integer> readIntPair(InputReader in) {
		int first = in.readInt();
		int second = in.readInt();
		return Pair.makePair(first, second);
	}

	public static Pair<Long, Long> readLongPair(InputReader in) {
		long first = in.readLong();
		long second = in.readLong();
		return Pair.makePair(first, second);
	}

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

	public static long[] readLongArray(InputReader in, int size) {
		long[] array = new long[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readLong();
		return array;
	}

	public static double[] readDoubleArray(InputReader in, int size) {
		double[] array = new double[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readDouble();
		return array;
	}

	public static String[] readStringArray(InputReader in, int size) {
		String[] array = new String[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readString();
		return array;
	}

	public static char[] readCharArray(InputReader in, int size) {
		char[] array = new char[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readCharacter();
		return array;
	}

	public static Pair<Integer, Integer>[] readIntPairArray(InputReader in,
			int size) {
		@SuppressWarnings({ "unchecked" })
		Pair<Integer, Integer>[] result = new Pair[size];
		for (int i = 0; i < size; i++)
			result[i] = readIntPair(in);
		return result;
	}

	public static Pair<Long, Long>[] readLongPairArray(InputReader in, int size) {
		@SuppressWarnings({ "unchecked" })
		Pair<Long, Long>[] result = new Pair[size];
		for (int i = 0; i < size; i++)
			result[i] = readLongPair(in);
		return result;
	}

	public static void readIntArrays(InputReader in, int[]... arrays) {
		for (int i = 0; i < arrays[0].length; i++) {
			for (int j = 0; j < arrays.length; j++)
				arrays[j][i] = in.readInt();
		}
	}

	public static void readLongArrays(InputReader in, long[]... arrays) {
		for (int i = 0; i < arrays[0].length; i++) {
			for (int j = 0; j < arrays.length; j++)
				arrays[j][i] = in.readLong();
		}
	}

	public static void readDoubleArrays(InputReader in, double[]... arrays) {
		for (int i = 0; i < arrays[0].length; i++) {
			for (int j = 0; j < arrays.length; j++)
				arrays[j][i] = in.readDouble();
		}
	}

	public static char[][] readTable(InputReader in, int rowCount,
			int columnCount) {
		char[][] table = new char[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readCharArray(in, columnCount);
		return table;
	}

	public static int[][] readIntTable(InputReader in, int rowCount,
			int columnCount) {
		int[][] table = new int[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readIntArray(in, columnCount);
		return table;
	}

	public static double[][] readDoubleTable(InputReader in, int rowCount,
			int columnCount) {
		double[][] table = new double[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readDoubleArray(in, columnCount);
		return table;
	}

	public static long[][] readLongTable(InputReader in, int rowCount,
			int columnCount) {
		long[][] table = new long[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readLongArray(in, columnCount);
		return table;
	}

	public static String[][] readStringTable(InputReader in, int rowCount,
			int columnCount) {
		String[][] table = new String[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readStringArray(in, columnCount);
		return table;
	}

	public static String readText(InputReader in) {
		StringBuilder result = new StringBuilder();
		while (true) {
			int character = in.read();
			if (character == '\r')
				continue;
			if (character == -1)
				break;
			result.append((char) character);
		}
		return result.toString();
	}

	public static void readStringArrays(InputReader in, String[]... arrays) {
		for (int i = 0; i < arrays[0].length; i++) {
			for (int j = 0; j < arrays.length; j++)
				arrays[j][i] = in.readString();
		}
	}

	public static void printTable(OutputWriter out, char[][] table) {
		for (char[] row : table)
			out.printLine(new String(row));
	}
}

interface IntComparator {
	public static final IntComparator DEFAULT = new IntComparator() {
		public int compare(int first, int second) {
			if (first < second)
				return -1;
			if (first > second)
				return 1;
			return 0;
		}
	};

	public static final IntComparator REVERSE = new IntComparator() {
		public int compare(int first, int second) {
			if (first < second)
				return 1;
			if (first > second)
				return -1;
			return 0;
		}
	};

	public int compare(int first, int second);
}

class BidirectionalGraph extends Graph {
	public int[] transposedEdge;

	public BidirectionalGraph(int vertexCount) {
		this(vertexCount, vertexCount);
	}

	public BidirectionalGraph(int vertexCount, int edgeCapacity) {
		super(vertexCount, 2 * edgeCapacity);
		transposedEdge = new int[2 * edgeCapacity];
	}

	public static BidirectionalGraph createGraph(int vertexCount, int[] from,
			int[] to) {
		BidirectionalGraph graph = new BidirectionalGraph(vertexCount,
				from.length);
		for (int i = 0; i < from.length; i++)
			graph.addSimpleEdge(from[i], to[i]);
		return graph;
	}

	public static BidirectionalGraph createWeightedGraph(int vertexCount,
			int[] from, int[] to, long[] weight) {
		BidirectionalGraph graph = new BidirectionalGraph(vertexCount,
				from.length);
		for (int i = 0; i < from.length; i++)
			graph.addWeightedEdge(from[i], to[i], weight[i]);
		return graph;
	}

	public static BidirectionalGraph createFlowGraph(int vertexCount,
			int[] from, int[] to, long[] capacity) {
		BidirectionalGraph graph = new BidirectionalGraph(vertexCount,
				from.length * 2);
		for (int i = 0; i < from.length; i++)
			graph.addFlowEdge(from[i], to[i], capacity[i]);
		return graph;
	}

	public static BidirectionalGraph createFlowWeightedGraph(int vertexCount,
			int[] from, int[] to, long[] weight, long[] capacity) {
		BidirectionalGraph graph = new BidirectionalGraph(vertexCount,
				from.length * 2);
		for (int i = 0; i < from.length; i++)
			graph.addFlowWeightedEdge(from[i], to[i], weight[i], capacity[i]);
		return graph;
	}

	@Override
	public int addEdge(int fromID, int toID, long weight, long capacity,
			int reverseEdge) {
		int lastEdgeCount = edgeCount;
		super.addEdge(fromID, toID, weight, capacity, reverseEdge);
		super.addEdge(toID, fromID, weight, capacity, reverseEdge == -1 ? -1
				: reverseEdge + 1);
		this.transposedEdge[lastEdgeCount] = lastEdgeCount + 1;
		this.transposedEdge[lastEdgeCount + 1] = lastEdgeCount;
		return lastEdgeCount;
	}

	@Override
	protected int entriesPerEdge() {
		return 2;
	}

	@Override
	public final int transposed(int id) {
		return transposedEdge[id];
	}

	@Override
	protected void ensureEdgeCapacity(int size) {
		if (size > edgeCapacity()) {
			super.ensureEdgeCapacity(size);
			transposedEdge = resize(transposedEdge, edgeCapacity());
		}
	}
}

class Graph {
	public static final int REMOVED_BIT = 0;

	protected int vertexCount;
	protected int edgeCount;

	private int[] firstOutbound;
	private int[] firstInbound;

	private Edge[] edges;
	private int[] nextInbound;
	private int[] nextOutbound;
	private int[] from;
	private int[] to;
	private long[] weight;
	private long[] capacity;
	private int[] reverseEdge;
	private int[] flags;

	public Graph(int vertexCount) {
		this(vertexCount, vertexCount);
	}

	public Graph(int vertexCount, int edgeCapacity) {
		this.vertexCount = vertexCount;
		firstOutbound = new int[vertexCount];
		Arrays.fill(firstOutbound, -1);

		from = new int[edgeCapacity];
		to = new int[edgeCapacity];
		nextOutbound = new int[edgeCapacity];
		flags = new int[edgeCapacity];
	}

	public static Graph createGraph(int vertexCount, int[] from, int[] to) {
		Graph graph = new Graph(vertexCount, from.length);
		for (int i = 0; i < from.length; i++)
			graph.addSimpleEdge(from[i], to[i]);
		return graph;
	}

	public static Graph createWeightedGraph(int vertexCount, int[] from,
			int[] to, long[] weight) {
		Graph graph = new Graph(vertexCount, from.length);
		for (int i = 0; i < from.length; i++)
			graph.addWeightedEdge(from[i], to[i], weight[i]);
		return graph;
	}

	public static Graph createFlowGraph(int vertexCount, int[] from, int[] to,
			long[] capacity) {
		Graph graph = new Graph(vertexCount, from.length * 2);
		for (int i = 0; i < from.length; i++)
			graph.addFlowEdge(from[i], to[i], capacity[i]);
		return graph;
	}

	public static Graph createFlowWeightedGraph(int vertexCount, int[] from,
			int[] to, long[] weight, long[] capacity) {
		Graph graph = new Graph(vertexCount, from.length * 2);
		for (int i = 0; i < from.length; i++)
			graph.addFlowWeightedEdge(from[i], to[i], weight[i], capacity[i]);
		return graph;
	}

	public static Graph createTree(int[] parent) {
		Graph graph = new Graph(parent.length + 1, parent.length);
		for (int i = 0; i < parent.length; i++)
			graph.addSimpleEdge(parent[i], i + 1);
		return graph;
	}

	public int addEdge(int fromID, int toID, long weight, long capacity,
			int reverseEdge) {
		ensureEdgeCapacity(edgeCount + 1);
		if (firstOutbound[fromID] != -1)
			nextOutbound[edgeCount] = firstOutbound[fromID];
		else
			nextOutbound[edgeCount] = -1;
		firstOutbound[fromID] = edgeCount;
		if (firstInbound != null) {
			if (firstInbound[toID] != -1)
				nextInbound[edgeCount] = firstInbound[toID];
			else
				nextInbound[edgeCount] = -1;
			firstInbound[toID] = edgeCount;
		}
		this.from[edgeCount] = fromID;
		this.to[edgeCount] = toID;
		if (capacity != 0) {
			if (this.capacity == null)
				this.capacity = new long[from.length];
			this.capacity[edgeCount] = capacity;
		}
		if (weight != 0) {
			if (this.weight == null)
				this.weight = new long[from.length];
			this.weight[edgeCount] = weight;
		}
		if (reverseEdge != -1) {
			if (this.reverseEdge == null) {
				this.reverseEdge = new int[from.length];
				Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
			}
			this.reverseEdge[edgeCount] = reverseEdge;
		}
		if (edges != null)
			edges[edgeCount] = createEdge(edgeCount);
		return edgeCount++;
	}

	protected final GraphEdge createEdge(int id) {
		return new GraphEdge(id);
	}

	public final int addFlowWeightedEdge(int from, int to, long weight,
			long capacity) {
		if (capacity == 0) {
			return addEdge(from, to, weight, 0, -1);
		} else {
			int lastEdgeCount = edgeCount;
			addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
			return addEdge(from, to, weight, capacity, lastEdgeCount);
		}
	}

	protected int entriesPerEdge() {
		return 1;
	}

	public final int addFlowEdge(int from, int to, long capacity) {
		return addFlowWeightedEdge(from, to, 0, capacity);
	}

	public final int addWeightedEdge(int from, int to, long weight) {
		return addFlowWeightedEdge(from, to, weight, 0);
	}

	public final int addSimpleEdge(int from, int to) {
		return addWeightedEdge(from, to, 0);
	}

	public final int vertexCount() {
		return vertexCount;
	}

	public final int edgeCount() {
		return edgeCount;
	}

	protected final int edgeCapacity() {
		return from.length;
	}

	public final Edge edge(int id) {
		initEdges();
		return edges[id];
	}

	public final int firstOutbound(int vertex) {
		int id = firstOutbound[vertex];
		while (id != -1 && isRemoved(id))
			id = nextOutbound[id];
		return id;
	}

	public final int nextOutbound(int id) {
		id = nextOutbound[id];
		while (id != -1 && isRemoved(id))
			id = nextOutbound[id];
		return id;
	}

	public final int firstInbound(int vertex) {
		initInbound();
		int id = firstInbound[vertex];
		while (id != -1 && isRemoved(id))
			id = nextInbound[id];
		return id;
	}

	public final int nextInbound(int id) {
		initInbound();
		id = nextInbound[id];
		while (id != -1 && isRemoved(id))
			id = nextInbound[id];
		return id;
	}

	public final int source(int id) {
		return from[id];
	}

	public final int destination(int id) {
		return to[id];
	}

	public final long weight(int id) {
		if (weight == null)
			return 0;
		return weight[id];
	}

	public final long capacity(int id) {
		if (capacity == null)
			return 0;
		return capacity[id];
	}

	public final long flow(int id) {
		if (reverseEdge == null)
			return 0;
		return capacity[reverseEdge[id]];
	}

	public final void pushFlow(int id, long flow) {
		if (flow == 0)
			return;
		if (flow > 0) {
			if (capacity(id) < flow)
				throw new IllegalArgumentException("Not enough capacity");
		} else {
			if (flow(id) < -flow)
				throw new IllegalArgumentException("Not enough capacity");
		}
		capacity[id] -= flow;
		capacity[reverseEdge[id]] += flow;
	}

	public int transposed(int id) {
		return -1;
	}

	public final int reverse(int id) {
		if (reverseEdge == null)
			return -1;
		return reverseEdge[id];
	}

	public final void addVertices(int count) {
		ensureVertexCapacity(vertexCount + count);
		Arrays.fill(firstOutbound, vertexCount, vertexCount + count, -1);
		if (firstInbound != null)
			Arrays.fill(firstInbound, vertexCount, vertexCount + count, -1);
		vertexCount += count;
	}

	protected final void initEdges() {
		if (edges == null) {
			edges = new Edge[from.length];
			for (int i = 0; i < edgeCount; i++)
				edges[i] = createEdge(i);
		}
	}

	public final void removeVertex(int vertex) {
		int id = firstOutbound[vertex];
		while (id != -1) {
			removeEdge(id);
			id = nextOutbound[id];
		}
		initInbound();
		id = firstInbound[vertex];
		while (id != -1) {
			removeEdge(id);
			id = nextInbound[id];
		}
	}

	private void initInbound() {
		if (firstInbound == null) {
			firstInbound = new int[firstOutbound.length];
			Arrays.fill(firstInbound, 0, vertexCount, -1);
			nextInbound = new int[from.length];
			for (int i = 0; i < edgeCount; i++) {
				nextInbound[i] = firstInbound[to[i]];
				firstInbound[to[i]] = i;
			}
		}
	}

	public final boolean flag(int id, int bit) {
		return (flags[id] >> bit & 1) != 0;
	}

	public final void setFlag(int id, int bit) {
		flags[id] |= 1 << bit;
	}

	public final void removeFlag(int id, int bit) {
		flags[id] &= -1 - (1 << bit);
	}

	public final void removeEdge(int id) {
		setFlag(id, REMOVED_BIT);
	}

	public final void restoreEdge(int id) {
		removeFlag(id, REMOVED_BIT);
	}

	public final boolean isRemoved(int id) {
		return flag(id, REMOVED_BIT);
	}

	public final Iterable<Edge> outbound(final int id) {
		initEdges();
		return new Iterable<Edge>() {
			public Iterator<Edge> iterator() {
				return new EdgeIterator(id, firstOutbound, nextOutbound);
			}
		};
	}

	public final Iterable<Edge> inbound(final int id) {
		initEdges();
		initInbound();
		return new Iterable<Edge>() {
			public Iterator<Edge> iterator() {
				return new EdgeIterator(id, firstInbound, nextInbound);
			}
		};
	}

	protected void ensureEdgeCapacity(int size) {
		if (from.length < size) {
			int newSize = Math.max(size, 2 * from.length);
			if (edges != null)
				edges = resize(edges, newSize);
			from = resize(from, newSize);
			to = resize(to, newSize);
			nextOutbound = resize(nextOutbound, newSize);
			if (nextInbound != null)
				nextInbound = resize(nextInbound, newSize);
			if (weight != null)
				weight = resize(weight, newSize);
			if (capacity != null)
				capacity = resize(capacity, newSize);
			if (reverseEdge != null)
				reverseEdge = resize(reverseEdge, newSize);
			flags = resize(flags, newSize);
		}
	}

	private void ensureVertexCapacity(int size) {
		if (firstOutbound.length < size) {
			int newSize = Math.max(size, 2 * from.length);
			firstOutbound = resize(firstOutbound, newSize);
			if (firstInbound != null)
				firstInbound = resize(firstInbound, newSize);
		}
	}

	protected final int[] resize(int[] array, int size) {
		int[] newArray = new int[size];
		System.arraycopy(array, 0, newArray, 0, array.length);
		return newArray;
	}

	private long[] resize(long[] array, int size) {
		long[] newArray = new long[size];
		System.arraycopy(array, 0, newArray, 0, array.length);
		return newArray;
	}

	private Edge[] resize(Edge[] array, int size) {
		Edge[] newArray = new Edge[size];
		System.arraycopy(array, 0, newArray, 0, array.length);
		return newArray;
	}

	public final boolean isSparse() {
		return vertexCount == 0 || edgeCount * 20 / vertexCount <= vertexCount;
	}

	protected class GraphEdge implements Edge {
		protected int id;

		protected GraphEdge(int id) {
			this.id = id;
		}

		public int getSource() {
			return source(id);
		}

		public int getDestination() {
			return destination(id);
		}

		public long getWeight() {
			return weight(id);
		}

		public long getCapacity() {
			return capacity(id);
		}

		public long getFlow() {
			return flow(id);
		}

		public void pushFlow(long flow) {
			Graph.this.pushFlow(id, flow);
		}

		public boolean getFlag(int bit) {
			return flag(id, bit);
		}

		public void setFlag(int bit) {
			Graph.this.setFlag(id, bit);
		}

		public void removeFlag(int bit) {
			Graph.this.removeFlag(id, bit);
		}

		public int getTransposedID() {
			return transposed(id);
		}

		public Edge getTransposedEdge() {
			int reverseID = getTransposedID();
			if (reverseID == -1)
				return null;
			initEdges();
			return edge(reverseID);
		}

		public int getReverseID() {
			return reverse(id);
		}

		public Edge getReverseEdge() {
			int reverseID = getReverseID();
			if (reverseID == -1)
				return null;
			initEdges();
			return edge(reverseID);
		}

		public int getID() {
			return id;
		}

		public void remove() {
			removeEdge(id);
		}

		public void restore() {
			restoreEdge(id);
		}
	}

	public class EdgeIterator implements Iterator<Edge> {
		private int edgeID;
		private final int[] next;
		private int lastID = -1;

		public EdgeIterator(int id, int[] first, int[] next) {
			this.next = next;
			edgeID = nextEdge(first[id]);
		}

		private int nextEdge(int id) {
			while (id != -1 && isRemoved(id))
				id = next[id];
			return id;
		}

		public boolean hasNext() {
			return edgeID != -1;
		}

		public Edge next() {
			if (edgeID == -1)
				throw new NoSuchElementException();
			lastID = edgeID;
			edgeID = nextEdge(next[lastID]);
			return edges[lastID];
		}

		public void remove() {
			if (lastID == -1)
				throw new IllegalStateException();
			removeEdge(lastID);
			lastID = -1;
		}
	}
}

class MiscUtils {
	public static final int[] DX4 = { 1, 0, -1, 0 };
	public static final int[] DY4 = { 0, -1, 0, 1 };
	public static final int[] DX8 = { 1, 1, 1, 0, -1, -1, -1, 0 };
	public static final int[] DY8 = { -1, 0, 1, 1, 1, 0, -1, -1 };
	public static final int[] DX_KNIGHT = { 2, 1, -1, -2, -2, -1, 1, 2 };
	public static final int[] DY_KNIGHT = { 1, 2, 2, 1, -1, -2, -2, -1 };

	private static final String[] ROMAN_TOKENS = { "M", "CM", "D", "CD", "C",
			"XC", "L", "XL", "X", "IX", "V", "IV", "I" };
	private static final int[] ROMAN_VALUES = { 1000, 900, 500, 400, 100, 90,
			50, 40, 10, 9, 5, 4, 1 };

	public static long josephProblem(long n, int k) {
		if (n == 1)
			return 0;
		if (k == 1)
			return n - 1;
		if (k > n)
			return (josephProblem(n - 1, k) + k) % n;
		long count = n / k;
		long result = josephProblem(n - count, k);
		result -= n % k;
		if (result < 0)
			result += n;
		else
			result += result / (k - 1);
		return result;
	}

	public static boolean isValidCell(int row, int column, int rowCount,
			int columnCount) {
		return row >= 0 && row < rowCount && column >= 0
				&& column < columnCount;
	}

	public static IntList getPath(int[] last, int destination) {
		IntList path = new IntArrayList();
		while (destination != -1) {
			path.add(destination);
			destination = last[destination];
		}
		path.inPlaceReverse();
		return path;
	}

	public static IntList getPath(int[][] lastIndex, int[][] lastPathNumber,
			int destination, int pathNumber) {
		IntList path = new IntArrayList();
		while (destination != -1 || pathNumber != 0) {
			path.add(destination);
			int nextDestination = lastIndex[destination][pathNumber];
			pathNumber = lastPathNumber[destination][pathNumber];
			destination = nextDestination;
		}
		path.inPlaceReverse();
		return path;
	}

	public static long maximalRectangleSum(long[][] array) {
		int n = array.length;
		int m = array[0].length;
		long[][] partialSums = new long[n + 1][m + 1];
		for (int i = 0; i < n; i++) {
			long rowSum = 0;
			for (int j = 0; j < m; j++) {
				rowSum += array[i][j];
				partialSums[i + 1][j + 1] = partialSums[i][j + 1] + rowSum;
			}
		}
		long result = Long.MIN_VALUE;
		for (int i = 0; i < m; i++) {
			for (int j = i; j < m; j++) {
				long minPartialSum = 0;
				for (int k = 1; k <= n; k++) {
					long current = partialSums[k][j + 1] - partialSums[k][i];
					result = Math.max(result, current - minPartialSum);
					minPartialSum = Math.min(minPartialSum, current);
				}
			}
		}
		return result;
	}

	public static int parseIP(String ip) {
		String[] components = ip.split("[.]");
		int result = 0;
		for (int i = 0; i < 4; i++)
			result += (1 << (24 - 8 * i)) * Integer.parseInt(components[i]);
		return result;
	}

	public static String buildIP(int mask) {
		StringBuilder result = new StringBuilder();
		for (int i = 0; i < 4; i++) {
			if (i != 0)
				result.append('.');
			result.append(mask >> (24 - 8 * i) & 255);
		}
		return result.toString();
	}

	public static long binarySearch(long from, long to,
			Function<Long, Boolean> function) {
		while (from < to) {
			long argument = from + (to - from) / 2;
			if (function.value(argument))
				to = argument;
			else
				from = argument + 1;
		}
		return from;
	}

	public static <T> boolean equals(T first, T second) {
		return first == null && second == null || first != null
				&& first.equals(second);
	}

	public static boolean isVowel(char ch) {
		ch = Character.toUpperCase(ch);
		return ch == 'A' || ch == 'E' || ch == 'I' || ch == 'O' || ch == 'U'
				|| ch == 'Y';
	}

	public static boolean isStrictVowel(char ch) {
		ch = Character.toUpperCase(ch);
		return ch == 'A' || ch == 'E' || ch == 'I' || ch == 'O' || ch == 'U';
	}

	public static String convertToRoman(int number) {
		StringBuilder result = new StringBuilder();
		for (int i = 0; i < ROMAN_TOKENS.length; i++) {
			while (number >= ROMAN_VALUES[i]) {
				number -= ROMAN_VALUES[i];
				result.append(ROMAN_TOKENS[i]);
			}
		}
		return result.toString();
	}

	public static int convertFromRoman(String number) {
		int result = 0;
		for (int i = 0; i < ROMAN_TOKENS.length; i++) {
			while (number.startsWith(ROMAN_TOKENS[i])) {
				number = number.substring(ROMAN_TOKENS[i].length());
				result += ROMAN_VALUES[i];
			}
		}
		return result;
	}

	public static int distance(int x1, int y1, int x2, int y2) {
		int dx = x1 - x2;
		int dy = y1 - y2;
		return dx * dx + dy * dy;
	}

	public static <T extends Comparable<T>> T min(T first, T second) {
		if (first.compareTo(second) <= 0)
			return first;
		return second;
	}

	public static <T extends Comparable<T>> T max(T first, T second) {
		if (first.compareTo(second) <= 0)
			return second;
		return first;
	}

	public static void decreaseByOne(int[]... arrays) {
		for (int[] array : arrays) {
			for (int i = 0; i < array.length; i++)
				array[i]--;
		}
	}

	public static int[] getIntArray(String s) {
		String[] tokens = s.split(" ");
		int[] result = new int[tokens.length];
		for (int i = 0; i < result.length; i++)
			result[i] = Integer.parseInt(tokens[i]);
		return result;
	}
}

class IntArrayList extends IntList {
	private int[] array;
	private int size;

	public IntArrayList() {
		this(10);
	}

	public IntArrayList(int capacity) {
		array = new int[capacity];
	}

	public IntArrayList(IntList list) {
		this(list.size());
		addAll(list);
	}

	@Override
	public int get(int index) {
		if (index >= size)
			throw new IndexOutOfBoundsException();
		return array[index];
	}

	@Override
	public void set(int index, int value) {
		if (index >= size)
			throw new IndexOutOfBoundsException();
		array[index] = value;
	}

	@Override
	public int size() {
		return size;
	}

	@Override
	public void add(int value) {
		ensureCapacity(size + 1);
		array[size++] = value;
	}

	public void ensureCapacity(int newCapacity) {
		if (newCapacity > array.length) {
			int[] newArray = new int[Math.max(newCapacity, array.length << 1)];
			System.arraycopy(array, 0, newArray, 0, size);
			array = newArray;
		}
	}

	@Override
	public int[] toArray() {
		int[] array = new int[size];
		System.arraycopy(this.array, 0, array, 0, size);
		return array;
	}

	@Override
	public int popBack() {
		return array[--size];
	}
}

abstract class IntList extends IntCollection implements Comparable<IntList> {
	private static final int INSERTION_THRESHOLD = 16;
	private static IntList EMPTY_LIST;

	public abstract int get(int index);

	public abstract void set(int index, int value);

	@Override
	public IntIterator iterator() {
		return new IntIterator() {
			private int size = size();
			private int index = 0;

			public int value() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				return get(index);
			}

			public void advance() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				index++;
			}

			public boolean isValid() {
				return index < size;
			}
		};
	}

	@Override
	public void remove(int value) {
		throw new UnsupportedOperationException();
	}

	public int find(int value) {
		int size = size();
		for (int i = 0; i < size; i++) {
			if (get(i) == value)
				return i;
		}
		return -1;
	}

	public int findLast(int value) {
		int size = size();
		for (int i = size - 1; i >= 0; i--) {
			if (get(i) == value)
				return i;
		}
		return -1;
	}

	public boolean nextPermutation() {
		return nextPermutation(IntComparator.DEFAULT);
	}

	private boolean nextPermutation(IntComparator comparator) {
		int size = size();
		int last = get(size - 1);
		for (int i = size - 2; i >= 0; i--) {
			int current = get(i);
			if (comparator.compare(last, current) > 0) {
				for (int j = size - 1; j > i; j--) {
					if (comparator.compare(get(j), current) > 0) {
						swap(i, j);
						subList(i + 1, size).inPlaceReverse();
						return true;
					}
				}
			}
			last = current;
		}
		return false;
	}

	public void inPlaceReverse() {
		for (int i = 0, j = size() - 1; i < j; i++, j--)
			swap(i, j);
	}

	public IntList subList(final int from, final int to) {
		return new SubList(from, to);
	}

	private void swap(int first, int second) {
		if (first == second)
			return;
		int temp = get(first);
		set(first, get(second));
		set(second, temp);
	}

	public IntSortedList inPlaceSort() {
		return inPlaceSort(IntComparator.DEFAULT);
	}

	public IntSortedList inPlaceSort(IntComparator comparator) {
		quickSort(0, size() - 1,
				(Integer.bitCount(Integer.highestOneBit(size()) - 1) * 5) >> 1,
				comparator);
		return new IntSortedArray(this, comparator);
	}

	private void quickSort(int from, int to, int remaining,
			IntComparator comparator) {
		if (to - from < INSERTION_THRESHOLD) {
			insertionSort(from, to, comparator);
			return;
		}
		if (remaining == 0) {
			heapSort(from, to, comparator);
			return;
		}
		remaining--;
		int pivotIndex = (from + to) >> 1;
		int pivot = get(pivotIndex);
		swap(pivotIndex, to);
		int storeIndex = from;
		int equalIndex = to;
		for (int i = from; i < equalIndex; i++) {
			int value = comparator.compare(get(i), pivot);
			if (value < 0)
				swap(storeIndex++, i);
			else if (value == 0)
				swap(--equalIndex, i--);
		}
		quickSort(from, storeIndex - 1, remaining, comparator);
		for (int i = equalIndex; i <= to; i++)
			swap(storeIndex++, i);
		quickSort(storeIndex, to, remaining, comparator);
	}

	private void heapSort(int from, int to, IntComparator comparator) {
		for (int i = (to + from - 1) >> 1; i >= from; i--)
			siftDown(i, to, comparator, from);
		for (int i = to; i > from; i--) {
			swap(from, i);
			siftDown(from, i - 1, comparator, from);
		}
	}

	private void siftDown(int start, int end, IntComparator comparator,
			int delta) {
		int value = get(start);
		while (true) {
			int child = ((start - delta) << 1) + 1 + delta;
			if (child > end)
				return;
			int childValue = get(child);
			if (child + 1 <= end) {
				int otherValue = get(child + 1);
				if (comparator.compare(otherValue, childValue) > 0) {
					child++;
					childValue = otherValue;
				}
			}
			if (comparator.compare(value, childValue) >= 0)
				return;
			swap(start, child);
			start = child;
		}
	}

	private void insertionSort(int from, int to, IntComparator comparator) {
		for (int i = from + 1; i <= to; i++) {
			int value = get(i);
			for (int j = i - 1; j >= from; j--) {
				if (comparator.compare(get(j), value) <= 0)
					break;
				swap(j, j + 1);
			}
		}
	}

	public IntSortedList sort() {
		return sort(IntComparator.DEFAULT);
	}

	public IntSortedList sort(IntComparator comparator) {
		return new IntArray(this).inPlaceSort(comparator);
	}

	public int back() {
		return get(size() - 1);
	}

	public int popBack() {
		throw new UnsupportedOperationException();
	}

	public int hashCode() {
		int hashCode = 1;
		for (IntIterator i = iterator(); i.isValid(); i.advance())
			hashCode = 31 * hashCode + i.value();
		return hashCode;
	}

	@Override
	public boolean equals(Object obj) {
		if (!(obj instanceof IntList))
			return false;
		IntList list = (IntList) obj;
		if (list.size() != size())
			return false;
		IntIterator i = iterator();
		IntIterator j = list.iterator();
		while (i.isValid()) {
			if (i.value() != j.value())
				return false;
			i.advance();
			j.advance();
		}
		return true;
	}

	public int compareTo(IntList o) {
		IntIterator i = iterator();
		IntIterator j = o.iterator();
		while (true) {
			if (i.isValid()) {
				if (j.isValid()) {
					if (i.value() != j.value()) {
						if (i.value() < j.value())
							return -1;
						else
							return 1;
					}
				} else
					return 1;
			} else {
				if (j.isValid())
					return -1;
				else
					return 0;
			}
			i.advance();
			j.advance();
		}
	}

	public static IntList emptyList() {
		if (EMPTY_LIST == null)
			EMPTY_LIST = new IntArray(new int[0]);
		return EMPTY_LIST;
	}

	private class SubList extends IntList {
		private final int to;
		private final int from;
		private int size;

		public SubList(int from, int to) {
			this.to = to;
			this.from = from;
			size = to - from;
		}

		@Override
		public int get(int index) {
			if (index < 0 || index >= size)
				throw new IndexOutOfBoundsException();
			return IntList.this.get(index + from);
		}

		@Override
		public void set(int index, int value) {
			if (index < 0 || index >= size)
				throw new IndexOutOfBoundsException();
			IntList.this.set(index + from, value);
		}

		@Override
		public int size() {
			return size;
		}

		@Override
		public void add(int value) {
			throw new UnsupportedOperationException();
		}
	}
}

class MinCostFlow {
	private final Graph graph;
	private final int source;
	private final int destination;
	private final long[] phi;
	private final long[] dijkstraResult;
	private final int[] lastEdge;
	private final Heap heap;
	private final int vertexCount;
	private final int[] visited;
	private int visitIndex;

	public MinCostFlow(Graph graph, int source, int destination,
			boolean hasNegativeEdges) {
		this.graph = graph;
		this.source = source;
		this.destination = destination;
		vertexCount = graph.vertexCount();
		phi = new long[vertexCount];
		if (hasNegativeEdges)
			fordBellman();
		dijkstraResult = new long[vertexCount];
		lastEdge = new int[vertexCount];
		if (graph.isSparse()) {
			heap = new Heap(vertexCount, new IntComparator() {
				public int compare(int first, int second) {
					return IntegerUtils.longCompare(dijkstraResult[first],
							dijkstraResult[second]);
				}
			}, vertexCount);
			visited = null;
		} else {
			heap = null;
			visited = new int[vertexCount];
		}
	}

	private void fordBellman() {
		Arrays.fill(phi, Long.MAX_VALUE);
		phi[source] = 0;
		boolean[] inQueue = new boolean[vertexCount];
		int[] queue = new int[vertexCount + 1];
		queue[0] = source;
		inQueue[source] = true;
		int stepCount = 0;
		int head = 0;
		int end = 1;
		int maxSteps = 2 * vertexCount * vertexCount;
		while (head != end) {
			int vertex = queue[head++];
			if (head == queue.length)
				head = 0;
			inQueue[vertex] = false;
			int edgeID = graph.firstOutbound(vertex);
			while (edgeID != -1) {
				long total = phi[vertex] + graph.weight(edgeID);
				int destination = graph.destination(edgeID);
				if (graph.capacity(edgeID) != 0 && phi[destination] > total) {
					phi[destination] = total;
					if (!inQueue[destination]) {
						queue[end++] = destination;
						inQueue[destination] = true;
						if (end == queue.length)
							end = 0;
					}
				}
				edgeID = graph.nextOutbound(edgeID);
			}
			if (++stepCount > maxSteps)
				throw new IllegalArgumentException(
						"Graph contains negative cycle");
		}
	}

	public static Pair<Long, Long> minCostMaxFlow(Graph graph, int source,
			int destination, boolean hasNegativeEdges) {
		return new MinCostFlow(graph, source, destination, hasNegativeEdges)
				.minCostMaxFlow();
	}

	public static Pair<Long, Long> minCostMaxFlow(Graph graph, int source,
			int destination, boolean hasNegativeEdges, long maxFlow) {
		return new MinCostFlow(graph, source, destination, hasNegativeEdges)
				.minCostMaxFlow(maxFlow);
	}

	public Pair<Long, Long> minCostMaxFlow() {
		return minCostMaxFlow(Long.MAX_VALUE);
	}

	public Pair<Long, Long> minCostMaxFlow(long maxFlow) {
		long cost = 0;
		long flow = 0;
		while (maxFlow != 0) {
			if (graph.isSparse())
				dijkstraAlgorithm();
			else
				dijkstraAlgorithmFull();
			if (lastEdge[destination] == -1)
				return Pair.makePair(cost, flow);
			for (int i = 0; i < dijkstraResult.length; i++) {
				if (dijkstraResult[i] != Long.MAX_VALUE)
					phi[i] += dijkstraResult[i];
			}
			int vertex = destination;
			long currentFlow = maxFlow;
			long currentCost = 0;
			while (vertex != source) {
				int edgeID = lastEdge[vertex];
				currentFlow = Math.min(currentFlow, graph.capacity(edgeID));
				currentCost += graph.weight(edgeID);
				vertex = graph.source(edgeID);
			}
			maxFlow -= currentFlow;
			cost += currentCost * currentFlow;
			flow += currentFlow;
			vertex = destination;
			while (vertex != source) {
				int edgeID = lastEdge[vertex];
				graph.pushFlow(edgeID, currentFlow);
				vertex = graph.source(edgeID);
			}
		}
		return Pair.makePair(cost, flow);
	}

	private void dijkstraAlgorithm() {
		Arrays.fill(dijkstraResult, Long.MAX_VALUE);
		Arrays.fill(lastEdge, -1);
		dijkstraResult[source] = 0;
		heap.add(source);
		while (!heap.isEmpty()) {
			int current = heap.poll();
			int edgeID = graph.firstOutbound(current);
			while (edgeID != -1) {
				if (graph.capacity(edgeID) != 0) {
					int next = graph.destination(edgeID);
					long total = graph.weight(edgeID) - phi[next]
							+ phi[current] + dijkstraResult[current];
					if (dijkstraResult[next] > total) {
						dijkstraResult[next] = total;
						if (heap.getIndex(next) == -1)
							heap.add(next);
						else
							heap.shiftUp(heap.getIndex(next));
						lastEdge[next] = edgeID;
					}
				}
				edgeID = graph.nextOutbound(edgeID);
			}
		}
	}

	private void dijkstraAlgorithmFull() {
		visitIndex++;
		Arrays.fill(dijkstraResult, Long.MAX_VALUE);
		lastEdge[destination] = -1;
		dijkstraResult[source] = 0;
		for (int i = 0; i < vertexCount; i++) {
			int index = -1;
			long length = Long.MAX_VALUE;
			for (int j = 0; j < vertexCount; j++) {
				if (visited[j] != visitIndex && dijkstraResult[j] < length) {
					length = dijkstraResult[j];
					index = j;
				}
			}
			if (index == -1) {
				return;
			}
			visited[index] = visitIndex;
			int edgeID = graph.firstOutbound(index);
			while (edgeID != -1) {
				if (graph.capacity(edgeID) != 0) {
					int next = graph.destination(edgeID);
					if (visited[next] != visitIndex) {
						long total = graph.weight(edgeID) - phi[next]
								+ phi[index] + length;
						if (dijkstraResult[next] > total) {
							dijkstraResult[next] = total;
							lastEdge[next] = edgeID;
						}
					}
				}
				edgeID = graph.nextOutbound(edgeID);
			}
		}
	}
}

class IntPair implements Comparable<IntPair> {
	public final int first, second;

	public IntPair(int first, int second) {
		this.first = first;
		this.second = second;
	}

	@Override
	public String toString() {
		return "(" + first + "," + second + ")";
	}

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

		IntPair intPair = (IntPair) o;

		return first == intPair.first && second == intPair.second;

	}

	@Override
	public int hashCode() {
		int result = first;
		result = 31 * result + second;
		return result;
	}

	public int compareTo(IntPair o) {
		if (first < o.first)
			return -1;
		if (first > o.first)
			return 1;
		if (second < o.second)
			return -1;
		if (second > o.second)
			return 1;
		return 0;
	}
}

class IntArray extends IntList {
	private final int[] array;

	public IntArray(int[] array) {
		this.array = array;
	}

	public IntArray(IntCollection collection) {
		array = new int[collection.size()];
		int i = 0;
		for (IntIterator iterator = collection.iterator(); iterator.isValid(); iterator
				.advance())
			array[i++] = iterator.value();
	}

	@Override
	public int get(int index) {
		return array[index];
	}

	@Override
	public void set(int index, int value) {
		array[index] = value;
	}

	@Override
	public int size() {
		return array.length;
	}

	@Override
	public void add(int value) {
		throw new UnsupportedOperationException();
	}

}

abstract class IntSortedList extends IntList {
	protected final IntComparator comparator;

	protected IntSortedList(IntComparator comparator) {
		this.comparator = comparator;
	}

	@Override
	public void set(int index, int value) {
		throw new UnsupportedOperationException();
	}

	@Override
	public void add(int value) {
		throw new UnsupportedOperationException();
	}

	protected void ensureSorted() {
		int size = size();
		if (size == 0)
			return;
		int last = get(0);
		for (int i = 1; i < size; i++) {
			int current = get(i);
			if (comparator.compare(last, current) > 0)
				throw new IllegalArgumentException();
			last = current;
		}
	}

}

interface Edge {

}

abstract class IntCollection {
	public abstract IntIterator iterator();

	public abstract int size();

	public abstract void add(int value);

	public abstract void remove(int value);

	public int[] toArray() {
		int size = size();
		int[] array = new int[size];
		int i = 0;
		for (IntIterator iterator = iterator(); iterator.isValid(); iterator
				.advance())
			array[i++] = iterator.value();
		return array;
	}

	public void addAll(IntCollection values) {
		for (IntIterator it = values.iterator(); it.isValid(); it.advance()) {
			add(it.value());
		}
	}

}

interface IntIterator {
	public int value() throws NoSuchElementException;

	public void advance() throws NoSuchElementException;

	public boolean isValid();
}

class IntSortedArray extends IntSortedList {
	private final int[] array;

	public IntSortedArray(IntCollection collection, IntComparator comparator) {
		super(comparator);
		array = new int[collection.size()];
		int i = 0;
		for (IntIterator iterator = collection.iterator(); iterator.isValid(); iterator
				.advance())
			array[i++] = iterator.value();
		ensureSorted();
	}

	@Override
	public int get(int index) {
		return array[index];
	}

	@Override
	public int size() {
		return array.length;
	}
}

class Pair<U, V> implements Comparable<Pair<U, V>> {
	public final U first;
	public final V second;

	public static <U, V> Pair<U, V> makePair(U first, V second) {
		return new Pair<U, V>(first, second);
	}

	private Pair(U first, V second) {
		this.first = first;
		this.second = second;
	}

	@SuppressWarnings({ "unchecked" })
	public int compareTo(Pair<U, V> o) {
		int value = ((Comparable<U>) first).compareTo(o.first);
		if (value != 0)
			return value;
		return ((Comparable<V>) second).compareTo(o.second);
	}
}

class Heap {
	private IntComparator comparator;
	private int size = 0;
	private int[] elements;
	private int[] at;

	public Heap(int capacity, IntComparator comparator, int maxElement) {
		this.comparator = comparator;
		elements = new int[capacity];
		at = new int[maxElement];
		Arrays.fill(at, -1);
	}

	public boolean isEmpty() {
		return size == 0;
	}

	public int add(int element) {
		ensureCapacity(size + 1);
		elements[size] = element;
		at[element] = size;
		shiftUp(size++);
		return at[element];
	}

	public void shiftUp(int index) {
		int value = elements[index];
		while (index != 0) {
			int parent = (index - 1) >>> 1;
			int parentValue = elements[parent];
			if (comparator.compare(parentValue, value) <= 0) {
				elements[index] = value;
				at[value] = index;
				return;
			}
			elements[index] = parentValue;
			at[parentValue] = index;
			index = parent;
		}
		elements[0] = value;
		at[value] = 0;
	}

	public void shiftDown(int index) {
		if (index < 0 || index >= size)
			throw new IllegalArgumentException();
		while (true) {
			int child = (index << 1) + 1;
			if (child >= size)
				return;
			if (child + 1 < size
					&& comparator.compare(elements[child], elements[child + 1]) > 0)
				child++;
			if (comparator.compare(elements[index], elements[child]) <= 0)
				return;
			swap(index, child);
			index = child;
		}
	}

	public int getIndex(int element) {
		return at[element];
	}

	private void swap(int first, int second) {
		int temp = elements[first];
		elements[first] = elements[second];
		elements[second] = temp;
		at[elements[first]] = first;
		at[elements[second]] = second;
	}

	private void ensureCapacity(int size) {
		if (elements.length < size) {
			int[] oldElements = elements;
			elements = new int[Math.max(2 * elements.length, size)];
			System.arraycopy(oldElements, 0, elements, 0, this.size);
		}
	}

	public int poll() {
		if (isEmpty())
			throw new IndexOutOfBoundsException();
		int result = elements[0];
		at[result] = -1;
		if (size == 1) {
			size = 0;
			return result;
		}
		elements[0] = elements[--size];
		at[elements[0]] = 0;
		shiftDown(0);
		return result;
	}

}

class IntegerUtils {

	public static int longCompare(long a, long b) {
		if (a < b)
			return -1;
		if (a > b)
			return 1;
		return 0;
	}

}

interface Function<A, V> {
	public abstract V value(A argument);
}