During the chemistry lesson Andrew learned that the saturated hydrocarbons (alkanes) enter into radical chlorination reaction. Andrew is a very curious boy, so he wondered how many different products of the reaction may be forms for a given alkane. He managed to solve the task for small molecules, but for large ones he faced some difficulties and asks you to help.

Formally, you are given a tree consisting of n vertices, such that the degree of each vertex doesn't exceed 4. You have to count the number of distinct non-isomorphic trees that can be obtained by adding to this tree one new vertex and one new edge, such that the graph is still the tree and the degree of each vertex doesn't exceed 4.

Two trees are isomorphic if there exists a bijection f(v) such that vertices u and v are connected by an edge if and only if vertices f(v) and f(u) are connected by an edge.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the number of vertices in the tree.

Then follow n - 1 lines with edges descriptions. Each edge is given by two integers ui and vi (1 ≤ ui, vi ≤ n) — indices of vertices connected by an edge. It's guaranteed that the given graph is a tree and the degree of each vertex doesn't exceed 4.

Output

Print one integer — the answer to the question.

Examples

Input

4
1 2
2 3
2 4


Output

2


Input

5
1 2
1 3
1 4
1 5


Output

1


Input

5
2 5
5 3
4 3
4 1


Output

3

Note

In the first sample, one can add new vertex to any existing vertex, but the trees we obtain by adding a new vertex to vertices 1, 3 and 4 are isomorphic, thus the answer is 2.

In the second sample, one can't add new vertex to the first vertex, as its degree is already equal to four. Trees, obtained by adding a new vertex to vertices 2, 3, 4 and 5 are isomorphic, thus the answer is 1.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;
import java.util.HashSet;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.Set;
import java.io.IOException;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
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);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        Graph graph;
        long[] hash1;
        long[] hash2;
        int[] size;
        int[] degree;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int[] u = new int[n - 1];
            int[] v = new int[n - 1];
            IOUtils.readIntArrays(in, u, v);
            MiscUtils.decreaseByOne(u, v);
            graph = BidirectionalGraph.createGraph(n, u, v);
            hash1 = new long[2 * n - 2];
            hash2 = new long[2 * n - 2];
            Arrays.fill(hash1, -1);
            Arrays.fill(hash2, -1);
            size = new int[2 * n - 2];
            Set<LongLongPair> distinct = new HashSet<>();
            long[] pow1 =
                    IntegerUtils.generatePowers(AbstractStringHash.MULTIPLIER, 2 * n + 1, AbstractStringHash.FIRST_MOD);
            long[] pow2 =
                    IntegerUtils.generatePowers(AbstractStringHash.MULTIPLIER, 2 * n + 1, AbstractStringHash.FIRST_MOD);
            degree = new int[n];
            for (int i = 0; i < n; i++) {
                for (int j = graph.firstOutbound(i); j != -1; j = graph.nextOutbound(j)) {
                    degree[i]++;
                }
            }
            for (int i = 0; i < n; i++) {
                if (degree[i] == 4) {
                    continue;
                }
                long res1 = calculateHash(i, -1, hash1, AbstractStringHash.FIRST_MOD, pow1).first;
                long res2 = calculateHash(i, -1, hash2, AbstractStringHash.SECOND_MOD, pow2).first;
                distinct.add(new LongLongPair(res1, res2));
            }
            out.printLine(distinct.size());
        }

        private LongIntPair calculateHash(int vertex, int last, long[] hash, long mod, long[] pow) {
            int length = last == -1 ? degree[vertex] : degree[vertex] - 1;
            long[] hDown = new long[length];
            int[] sDown = new int[length];
            int at = 0;
            for (int i = graph.firstOutbound(vertex); i != -1; i = graph.nextOutbound(i)) {
                int next = graph.destination(i);
                if (next == last) {
                    continue;
                }
                if (hash[i] == -1) {
                    LongIntPair pair = calculateHash(next, vertex, hash, mod, pow);
                    hash[i] = pair.first;
                    size[i] = pair.second;
                }
                hDown[at] = hash[i];
                sDown[at++] = size[i];
            }
            int[] order = ArrayUtils.order(hDown);
            long result = 0;
            int size = 1;
            for (int i : order) {
                result += pow[size] * hDown[i] % mod;
                size += sDown[i];
            }
            result += pow[size++];
            result %= mod;
            return new LongIntPair(result, size);
        }

    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.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 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 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;
        }

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

        }

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();

        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }

    static 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 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;
        }


        protected int entriesPerEdge() {
            return 2;
        }


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

    }

    static class Sorter {
        private static final int INSERTION_THRESHOLD = 16;

        private Sorter() {
        }

        public static void sort(IntList list, IntComparator comparator) {
            quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1,
                    comparator);
        }

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

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

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

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

    }

    static abstract class AbstractStringHash implements StringHash {
        public static final long MULTIPLIER;
        protected static final long FIRST_REVERSE_MULTIPLIER;
        protected static final long SECOND_REVERSE_MULTIPLIER;
        public static final long FIRST_MOD;
        public static final long SECOND_MOD;

        static {
            Random random = new Random(System.currentTimeMillis());
            FIRST_MOD = IntegerUtils.nextPrime((long) (1e9 + random.nextInt((int) 1e9)));
            SECOND_MOD = IntegerUtils.nextPrime((long) (1e9 + random.nextInt((int) 1e9)));
            MULTIPLIER = random.nextInt((int) 1e9 - 257) + 257;
            FIRST_REVERSE_MULTIPLIER = IntegerUtils.reverse(MULTIPLIER, FIRST_MOD);
            SECOND_REVERSE_MULTIPLIER = IntegerUtils.reverse(MULTIPLIER, SECOND_MOD);
        }
    }

    static interface IntReversableCollection extends IntCollection {
    }

    static class IntArray extends IntAbstractStream implements IntList {
        private int[] data;

        public IntArray(int[] arr) {
            data = arr;
        }

        public int size() {
            return data.length;
        }

        public int get(int at) {
            return data[at];
        }

        public void addAt(int index, int value) {
            throw new UnsupportedOperationException();
        }

        public void removeAt(int index) {
            throw new UnsupportedOperationException();
        }

        public void set(int index, int value) {
            data[index] = value;
        }

    }

    static interface StringHash {
    }

    static class LongIntPair implements Comparable<LongIntPair> {
        public final long first;
        public final int second;

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


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

            LongIntPair pair = (LongIntPair) o;

            return first == pair.first && second == pair.second;
        }


        public int hashCode() {
            int result = Long.hashCode(first);
            result = 31 * result + Integer.hashCode(second);
            return result;
        }


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

        @SuppressWarnings({"unchecked"})
        public int compareTo(LongIntPair o) {
            int value = Long.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }

    }

    static abstract class IntAbstractStream implements IntStream {

        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }


        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }


        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }

    static class Range {
        public static IntList range(int from, int to) {
            int[] result = new int[Math.abs(from - to)];
            int current = from;
            if (from <= to) {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current++;
                }
            } else {
                for (int i = 0; i < result.length; i++) {
                    result[i] = current--;
                }
            }
            return new IntArray(result);
        }

    }

    static class ArrayUtils {
        public static int[] range(int from, int to) {
            return Range.range(from, to).toArray();
        }

        public static int[] createOrder(int size) {
            return range(0, size);
        }

        public static int[] sort(int[] array, IntComparator comparator) {
            return sort(array, 0, array.length, comparator);
        }

        public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
            if (from == 0 && to == array.length) {
                new IntArray(array).sort(comparator);
            } else {
                new IntArray(array).subList(from, to).sort(comparator);
            }
            return array;
        }

        public static int[] order(final long[] array) {
            return sort(createOrder(array.length), new IntComparator() {
                public int compare(int first, int second) {
                    if (array[first] < array[second]) {
                        return -1;
                    }
                    if (array[first] > array[second]) {
                        return 1;
                    }
                    return 0;
                }
            });
        }

    }

    static interface IntComparator {
        public int compare(int first, int second);

    }

    static interface Edge {
    }

    static class LongLongPair implements Comparable<LongLongPair> {
        public final long first;
        public final long second;

        public LongLongPair(long first, long second) {
            this.first = first;
            this.second = second;
        }


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

            LongLongPair pair = (LongLongPair) o;

            return first == pair.first && second == pair.second;
        }


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


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

        @SuppressWarnings({"unchecked"})
        public int compareTo(LongLongPair o) {
            int value = Long.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Long.compare(second, o.second);
        }

    }

    static interface IntCollection extends IntStream {
        public int size();

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

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

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

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

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

        public abstract void removeAt(int index);

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

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }


        default public void add(int value) {
            addAt(size(), value);
        }

        default public IntList sort(IntComparator comparator) {
            Sorter.sort(this, comparator);
            return this;
        }

        default public IntList subList(final int from, final int to) {
            return new IntList() {
                private final int shift;
                private final int size;

                {
                    if (from < 0 || from > to || to > IntList.this.size()) {
                        throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
                    }
                    shift = from;
                    size = to - from;
                }

                public int size() {
                    return size;
                }

                public int get(int at) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    return IntList.this.get(at + shift);
                }

                public void addAt(int index, int value) {
                    throw new UnsupportedOperationException();
                }

                public void removeAt(int index) {
                    throw new UnsupportedOperationException();
                }

                public void set(int at, int value) {
                    if (at < 0 || at >= size) {
                        throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
                    }
                    IntList.this.set(at + shift, value);
                }

                public IntList compute() {
                    return new IntArrayList(this);
                }
            };
        }

    }

    static 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 close() {
            writer.close();
        }

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

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

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

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if (index > size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if (index >= size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size - 1) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

    }

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

    }

    static class IntegerUtils {
        public static long power(long base, long exponent, long mod) {
            if (base >= mod) {
                base %= mod;
            }
            if (exponent == 0) {
                return 1 % mod;
            }
            long result = power(base, exponent >> 1, mod);
            result = result * result % mod;
            if ((exponent & 1) != 0) {
                result = result * base % mod;
            }
            return result;
        }

        public static long reverse(long number, long module) {
            return power(number, module - 2, module);
        }

        public static boolean isPrime(long number) {
            if (number < 2) {
                return false;
            }
            for (long i = 2; i * i <= number; i++) {
                if (number % i == 0) {
                    return false;
                }
            }
            return true;
        }

        public static long[] generatePowers(long base, int count, long mod) {
            long[] result = new long[count];
            if (count != 0) {
                result[0] = 1 % mod;
            }
            for (int i = 1; i < count; i++) {
                result[i] = result[i - 1] * base % mod;
            }
            return result;
        }

        public static long nextPrime(long from) {
            if (from <= 2) {
                return 2;
            }
            from += 1 - (from & 1);
            while (!isPrime(from)) {
                from += 2;
            }
            return from;
        }

    }

    static 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;
        public 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 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 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);
        }

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

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

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

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

        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);
            }
        }

        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;
        }

        protected class GraphEdge implements Edge {
            protected int id;

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

        }

    }

    static class IOUtils {
        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();
                }
            }
        }

    }
}

