Problem: Ralph is going to collect mushrooms in the Mushroom Forest. 

There are m directed paths connecting n trees in the Mushroom Forest. On each path grow some mushrooms. When Ralph passes a path, he collects all the mushrooms on the path. The Mushroom Forest has a magical fertile ground where mushrooms grow at a fantastic speed. New mushrooms regrow as soon as Ralph finishes mushroom collection on a path. More specifically, after Ralph passes a path the i-th time, there regrow i mushrooms less than there was before this pass. That is, if there is initially x mushrooms on a path, then Ralph will collect x mushrooms for the first time, x - 1 mushrooms the second time, x - 1 - 2 mushrooms the third time, and so on. However, the number of mushrooms can never be less than 0.

For example, let there be 9 mushrooms on a path initially. The number of mushrooms that can be collected from the path is 9, 8, 6 and 3 when Ralph passes by from first to fourth time. From the fifth time and later Ralph can't collect any mushrooms from the path (but still can pass it).

Ralph decided to start from the tree s. How many mushrooms can he collect using only described paths?

Input

The first line contains two integers n and m (1 ≤ n ≤ 106, 0 ≤ m ≤ 106), representing the number of trees and the number of directed paths in the Mushroom Forest, respectively.

Each of the following m lines contains three integers x, y and w (1 ≤ x, y ≤ n, 0 ≤ w ≤ 108), denoting a path that leads from tree x to tree y with w mushrooms initially. There can be paths that lead from a tree to itself, and multiple paths between the same pair of trees.

The last line contains a single integer s (1 ≤ s ≤ n) — the starting position of Ralph. 

Output

Print an integer denoting the maximum number of the mushrooms Ralph can collect during his route. 

Examples

Input

2 2
1 2 4
2 1 4
1


Output

16

Input

3 3
1 2 4
2 3 3
1 3 8
1


Output

8

Note

In the first sample Ralph can pass three times on the circle and collect 4 + 4 + 3 + 3 + 1 + 1 = 16 mushrooms. After that there will be no mushrooms for Ralph to collect.

In the second sample, Ralph can go to tree 3 and collect 8 mushrooms on the path from tree 1 to tree 3.

Solution (in JAVA):

Solution:
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.ArrayList;
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.io.IOException;
import java.io.Writer;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cacophonix
 */
public class Main {
    public static void main(String[] args) {
        
        //TaskE solver = new TaskE();
        new Thread(null, new TaskE(), "whatever", 1<<28).start();
        
    }

    static class TaskE implements Runnable {

        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            InputReader in = new InputReader(inputStream);
            OutputWriter out = new OutputWriter(outputStream);
            solve(1, in, out); 
            out.close();
        }

        Graph graph;

        int n;
        int m;
        int x;
        int y;
        int[] from;
        int[] to;
        int[] mashrooms;
        long ans;
        int[] color;
        //ArrayList<IntIntPair>[] eds;
        ArrayList<IntIntPair> edges;
        long[] visited;
        long[] sum_by_color;

        long fun(long w) {
            long lo = 0;
            long hi = 100000002;
            long mid;
            while (lo < hi) {
                mid = (lo + hi) >> 1;
                if (mid * mid + mid >= 2 * w) {
                    hi = mid;
                } else {
                    lo = mid + 1;
                }
            }
            return hi * w - hi * (hi - 1) * (hi + 1) / 6;

        }

        long fun_max(int node) {


            if (visited[node] != -1) {
                return visited[node];
            }

            visited[node] = 0;
            
            // int edgeID = graph.firstOutbound(vertexID);
            // while (edgeID != -1) {
            //     firstDFS(graph.destination(edgeID));
            //     edgeID = graph.nextOutbound(edgeID);
            // }

            int ed = graph.firstOutbound(node);
            // System.out.println(node);
            // System.out.println(node);
            // for(int i=0;i<mashrooms.length;i++)System.out.print(mashrooms[i]+" ");
            // System.out.println();
            // for(int i=0;i<graph.capacity.length;i++)System.out.print(graph.capacity[i]+" ");
            // System.out.println();
            while (ed!=-1) {
                //System.out.println(ed);
                visited[node] = Math.max(visited[node], graph.weight(ed) + fun_max(graph.destination(ed)));
                ed = graph.nextOutbound(ed);
            }

            visited[node] += sum_by_color[node];

            return visited[node];
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.readInt();
            m = in.readInt();
            //n = 1000000;
            //m = 1000000;


            sum_by_color = new long[n + 1];
            visited = new long[n];
            Arrays.fill(visited, -1);
            edges = new ArrayList<>();
            mashrooms = new int[m];
            from = new int[m];
            to = new int[m];
            //eds = new ArrayList[n];

            // for (int i = 0; i < n; i++) {
            //     eds[i] = new ArrayList<>();
            // }

            graph = new Graph(n, m);
            for (int i = 0; i < m; i++) {
                x = in.readInt();
                //x=(int)(Math.random()*n);
                x--;
                y = in.readInt();
                //y = (int)(Math.random()*n);
                y--;
                //if(x==y)y++;
                from[i] = x;
                to[i] = y;
                mashrooms[i] = in.readInt();
                //mashrooms[i] = (int)(Math.random()*n);
                graph.addSimpleEdge(x, y);
            }

            color = StronglyConnectedComponents.kosaraju(graph);
            ans = 0;
            for (int i = 0; i < m; i++) {
                if (color[from[i]] == color[to[i]]) {
                    sum_by_color[color[from[i]]] += fun(mashrooms[i]);
                }
            }


            for (int i = 0; i < m; i++) {
                edges.add(IntIntPair.makePair(mashrooms[i], i));
            }
            // if (n == 999999) {
            //     return;
            // }

            Collections.sort(edges);

            graph = new Graph(n, m);


            for (int i = 0; i < m; i++) {

                int ii = edges.get(i).second;
                
                

                x = color[from[ii]];
                y = color[to[ii]];
                if (x == y) continue;

                graph.addWeightedEdge(x, y, mashrooms[ii]);

                //eds[x].add(IntIntPair.makePair(y, ii));


            }
            x = in.readInt();
            //x = 0;
            x--;
            ans += fun_max(color[x]);

            out.printLine(ans);

        }

    }

    static class StronglyConnectedComponents {
        private final Graph graph;
        private int[] order;
        private boolean[] visited;
        private int index = 0;
        private int vertexCount;
        private int[] condensed;
        private IntSet next;

        private StronglyConnectedComponents(Graph graph) {
            this.graph = graph;
            vertexCount = graph.vertexCount();
            order = new int[vertexCount];
            visited = new boolean[vertexCount];
            condensed = new int[vertexCount];
        }

        public static int[] kosaraju(Graph graph) {
            return new StronglyConnectedComponents(graph).kosaraju();
        }

        private int[] kosaraju() {
            for (int i = 0; i < vertexCount; i++) {
                if (!visited[i]) {
                    firstDFS(i);
                }
            }
            Arrays.fill(visited, false);
            //Graph result = new Graph(0);
            index = 0;
            for (int i = vertexCount - 1; i >= 0; i--) {
                if (!visited[order[i]]) {
                    //next = new IntHashSet();
                    secondDFS(order[i]);
                    //result.addVertices(1);
                    // for (int set : next.toArray()) {
                    //     result.addSimpleEdge(set, index);
                    // }
                    index++;
                }
            }
            return condensed;
        }

        private void secondDFS(int vertexID) {
            if (visited[vertexID]) {
                // if (condensed[vertexID] != index) {
                //     next.add(condensed[vertexID]);
                // }
                return;
            }
            condensed[vertexID] = index;
            visited[vertexID] = true;
            int edgeID = graph.firstInbound(vertexID);
            while (edgeID != -1) {
                secondDFS(graph.source(edgeID));
                edgeID = graph.nextInbound(edgeID);
            }
        }

        private void firstDFS(int vertexID) {
            if (visited[vertexID]) {
                return;
            }
            visited[vertexID] = true;
            int edgeID = graph.firstOutbound(vertexID);
            while (edgeID != -1) {
                firstDFS(graph.destination(edgeID));
                edgeID = graph.nextOutbound(edgeID);
            }
            order[index++] = vertexID;
        }

    }

    static 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;
        }


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

            Pair pair = (Pair) o;

            return !(first != null ? !first.equals(pair.first) : pair.first != null) &&
                    !(second != null ? !second.equals(pair.second) : pair.second != null);
        }


        public int hashCode() {
            int result = first != null ? first.hashCode() : 0;
            result = 31 * result + (second != null ? second.hashCode() : 0);
            return result;
        }


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

    }

    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 Edge {
    }

    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 IntHashSet extends IntAbstractStream implements IntSet {
        private static final Random RND = new Random();
        private static final int[] SHIFTS = new int[4];
        private static final byte PRESENT_MASK = 1;
        private static final byte REMOVED_MASK = 2;
        private int size;
        private int realSize;
        private int[] values;
        private byte[] present;
        private int step;
        private int ratio;

        static {
            for (int i = 0; i < 4; i++) {
                SHIFTS[i] = RND.nextInt(31) + 1;
            }
        }

        public IntHashSet() {
            this(3);
        }

        public IntHashSet(int capacity) {
            capacity = Math.max(capacity, 3);
            values = new int[capacity];
            present = new byte[capacity];
            ratio = 2;
            initStep(capacity);
        }

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

        public IntHashSet(int[] arr) {
            this(new IntArray(arr));
        }

        private void initStep(int capacity) {
            step = RND.nextInt(capacity - 2) + 1;
            while (IntegerUtils.gcd(step, capacity) != 1) {
                step++;
            }
        }


        public IntIterator intIterator() {
            return new IntIterator() {
                private int position = size == 0 ? values.length : -1;

                public int value() throws NoSuchElementException {
                    if (position == -1) {
                        advance();
                    }
                    if (position >= values.length) {
                        throw new NoSuchElementException();
                    }
                    if ((present[position] & PRESENT_MASK) == 0) {
                        throw new IllegalStateException();
                    }
                    return values[position];
                }

                public boolean advance() throws NoSuchElementException {
                    if (position >= values.length) {
                        throw new NoSuchElementException();
                    }
                    position++;
                    while (position < values.length && (present[position] & PRESENT_MASK) == 0) {
                        position++;
                    }
                    return isValid();
                }

                public boolean isValid() {
                    return position < values.length;
                }

                public void remove() {
                    if ((present[position] & PRESENT_MASK) == 0) {
                        throw new IllegalStateException();
                    }
                    present[position] = REMOVED_MASK;
                }
            };
        }


        public int size() {
            return size;
        }


        public void add(int value) {
            ensureCapacity((realSize + 1) * ratio + 2);
            int current = getHash(value);
            while (present[current] != 0) {
                if ((present[current] & PRESENT_MASK) != 0 && values[current] == value) {
                    return;
                }
                current += step;
                if (current >= values.length) {
                    current -= values.length;
                }
            }
            while ((present[current] & PRESENT_MASK) != 0) {
                current += step;
                if (current >= values.length) {
                    current -= values.length;
                }
            }
            if (present[current] == 0) {
                realSize++;
            }
            present[current] = PRESENT_MASK;
            values[current] = value;
            size++;
        }

        private int getHash(int value) {
            int hash = IntHash.hash(value);
            int result = hash;
            for (int i : SHIFTS) {
                result ^= hash >> i;
            }
            result %= values.length;
            if (result < 0) {
                result += values.length;
            }
            return result;
        }

        private void ensureCapacity(int capacity) {
            if (values.length < capacity) {
                capacity = Math.max(capacity * 2, values.length);
                rebuild(capacity);
            }
        }

        private void rebuild(int capacity) {
            initStep(capacity);
            int[] oldValues = values;
            byte[] oldPresent = present;
            values = new int[capacity];
            present = new byte[capacity];
            size = 0;
            realSize = 0;
            for (int i = 0; i < oldValues.length; i++) {
                if ((oldPresent[i] & PRESENT_MASK) == PRESENT_MASK) {
                    add(oldValues[i]);
                }
            }
        }

    }

    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(long i) {
            writer.println(i);
        }

    }

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

        public static IntIntPair makePair(int first, int second) {
            return new IntIntPair(first, second);
        }

        public IntIntPair(int 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;
            }

            IntIntPair pair = (IntIntPair) o;

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


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


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

        @SuppressWarnings({"unchecked"})
        public int compareTo(IntIntPair o) {
            int value = Integer.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 interface IntSet extends IntCollection {
    }

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

        public final int vertexCount() {
            return vertexCount;
        }

        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 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;
        }

        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 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);
            }
        }

        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;
        }

        protected class GraphEdge implements Edge {
            protected int id;

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

        }

    }

    static class IntegerUtils {
        public static int gcd(int a, int b) {
            a = Math.abs(a);
            b = Math.abs(b);
            while (b != 0) {
                int temp = a % b;
                a = b;
                b = temp;
            }
            return a;
        }

    }

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

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

        public abstract void removeAt(int index);

        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);
        }

    }

    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 IntReversableCollection extends IntCollection {
    }

    static class IntHash {
        private IntHash() {
        }

        public static int hash(int c) {
            return c;
        }

    }

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

        public boolean advance();

        public boolean isValid();

    }

    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();
        }

    }
}