Problem: Andrew and Eugene are playing a game. Initially, Andrew has string s, consisting of digits. Eugene sends Andrew multiple queries of type "di → ti", that means "replace all digits di in string s with substrings equal to ti". For example, if s = 123123, then query "2 → 00" transforms s to 10031003, and query "3 → " ("replace 3 by an empty string") transforms it to s = 1212. After all the queries Eugene asks Andrew to find the remainder after division of number with decimal representation equal to s by 1000000007 (109 + 7). When you represent s as a decimal number, please ignore the leading zeroes; also if s is an empty string, then it's assumed that the number equals to zero.

Andrew got tired of processing Eugene's requests manually and he asked you to write a program for that. Help him!

Input

The first line contains string s (1 ≤ |s| ≤ 105), consisting of digits — the string before processing all the requests.

The second line contains a single integer n (0 ≤ n ≤ 105) — the number of queries.

The next n lines contain the descriptions of the queries. The i-th query is described by string "di->ti", where di is exactly one digit (from 0 to 9), ti is a string consisting of digits (ti can be an empty string). The sum of lengths of ti for all queries doesn't exceed 105. The queries are written in the order in which they need to be performed.

Output

Print a single integer — remainder of division of the resulting number by 1000000007 (109 + 7).

Examples

Input

123123
1
2-&gt;00


Output

10031003


Input

123123
1
3-&gt;


Output

1212


Input

222
2
2-&gt;0
0-&gt;7


Output

777


Input

1000000008
0


Output

1

Note

Note that the leading zeroes are not removed from string s after the replacement (you can see it in the third sample).

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.util.*;

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 Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {
    
    void solve(int testNumber, InputReader in, OutputWriter out) {
        long[] size=new long[10], value=new long[10];
        Arrays.fill(size, 10);
        for (int i=0; i<10; i++) value[i]=i;
        char[] str=in.readString().toCharArray();
        int n=in.readInt(), MOD=1_000_000_007;
        char[] letter=new char[n+1];
        char[][] string=new char[n+1][];
        string[0]=str;
        letter[0]='0';
        for (int i=1; i<=n; i++) {
            String aux=in.readString();
            letter[i]=aux.charAt(0);
            string[i]=aux.substring(3).toCharArray();
        }
        for (int i=n; i>=0; i--) {
            long v=0, s=1;
            for (char j: string[i]) {
                v=(size[j-'0']*v%MOD+value[j-'0'])%MOD;
                s=s*size[j-'0']%MOD;
            }
            size[letter[i]-'0']=s;
            value[letter[i]-'0']=v;
        }
        out.printLine(value[0]);
    }
}

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 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;
        }
    }

}

interface Edge {
    public int getSource();

    public int getDestination();

    public long getWeight();

    public long getCapacity();

    public long getFlow();

    public void pushFlow(long flow);

    public boolean getFlag(int bit);

    public void setFlag(int bit);

    public void removeFlag(int bit);

    public int getTransposedID();

    public Edge getTransposedEdge();

    public int getReverseID();

    public Edge getReverseEdge();

    public int getID();

    public void remove();

    public void restore();
}

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

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

class IntegerUtils {

    public static List<Pair<Long, Integer>> factorize(long number) {
        List<Pair<Long, Integer>> result = new ArrayList<Pair<Long, Integer>>();
        for (long i = 2; i * i <= number; i++) {
            if (number % i == 0) {
                int power = 0;
                do {
                    power++;
                    number /= i;
                } while (number % i == 0);
                result.add(Pair.makePair(i, power));
            }
        }
        if (number != 1)
            result.add(Pair.makePair(number, 1));
        return result;
    }

    public static List<Long> getDivisors(long number) {
        List<Pair<Long, Integer>> primeDivisors = factorize(number);
        return getDivisorsImpl(primeDivisors, 0, 1, new ArrayList<Long>());
    }

    private static List<Long> getDivisorsImpl(
            List<Pair<Long, Integer>> primeDivisors, int index, long current,
            List<Long> result) {
        if (index == primeDivisors.size()) {
            result.add(current);
            return result;
        }
        long p = primeDivisors.get(index).first;
        int power = primeDivisors.get(index).second;
        for (int i = 0; i <= power; i++) {
            getDivisorsImpl(primeDivisors, index + 1, current, result);
            current *= p;
        }
        return result;
    }
}

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;
    }

    @Override
    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);

    }

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

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

    @Override
    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);
    }
}

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

    public void printLine(long[] array) {
        print(array);
        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 ArrayUtils {

    public static int[] createOrder(int size) {
        int[] order = new int[size];
        for (int i = 0; i < size; i++)
            order[i] = i;
        return order;
    }

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

    public static int maxPosition(int[] array, int from, int to) {
        if (from >= to)
            return -1;
        int max = array[from];
        int result = from;
        for (int i = from + 1; i < to; i++) {
            if (array[i] > max) {
                max = array[i];
                result = i;
            }
        }
        return result;
    }

}