Once Vasya and Petya assembled a figure of m cubes, each of them is associated with a number between 0 and m - 1 (inclusive, each number appeared exactly once). Let's consider a coordinate system such that the OX is the ground, and the OY is directed upwards. Each cube is associated with the coordinates of its lower left corner, these coordinates are integers for each cube.

The figure turned out to be stable. This means that for any cube that is not on the ground, there is at least one cube under it such that those two cubes touch by a side or a corner. More formally, this means that for the cube with coordinates (x, y) either y = 0, or there is a cube with coordinates (x - 1, y - 1), (x, y - 1) or (x + 1, y - 1).

Now the boys want to disassemble the figure and put all the cubes in a row. In one step the cube is removed from the figure and being put to the right of the blocks that have already been laid. The guys remove the cubes in such order that the figure remains stable. To make the process more interesting, the guys decided to play the following game. The guys take out the cubes from the figure in turns. It is easy to see that after the figure is disassembled, the integers written on the cubes form a number, written in the m-ary positional numerical system (possibly, with a leading zero). Vasya wants the resulting number to be maximum possible, and Petya, on the contrary, tries to make it as small as possible. Vasya starts the game.

Your task is to determine what number is formed after the figure is disassembled, if the boys play optimally. Determine the remainder of the answer modulo 109 + 9.

Input

The first line contains number m (2 ≤ m ≤ 105).

The following m lines contain the coordinates of the cubes xi, yi ( - 109 ≤ xi ≤ 109, 0 ≤ yi ≤ 109) in ascending order of numbers written on them. It is guaranteed that the original figure is stable.

No two cubes occupy the same place.

Output

In the only line print the answer to the problem.

Examples

Input

3
2 1
1 0
0 1


Output

19


Input

5
0 0
0 1
0 2
0 3
0 4


Output

2930
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.TreeSet;
import java.util.ArrayList;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.util.Map.Entry;
import java.io.Writer;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BCubes solver = new BCubes();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BCubes {
        TreeSet<Node> pq = new TreeSet<>(Comparator.comparingInt(x -> x.id));
        Debug debug = new Debug(true);

        public void decreaseOutDeg(Node root, int mod) {
            if (root.removed) {
                return;
            }
            root.outdeg -= mod;
            if (root.outdeg == 1) {
                for (Node node : root.out) {
                    if (node.removed) {
                        continue;
                    }
                    node.indeg++;
                    if (node.indeg == 1) {
                        pq.remove(node);
                    }
                }
            }
        }

        public void removeNode(Node root) {
            assert !root.removed;
            root.removed = true;
            if (root.outdeg == 1) {
                int cnt = 0;
                for (Node node : root.out) {
                    if (node.removed) {
                        continue;
                    }
                    cnt++;
                    node.indeg--;
                    if (node.indeg == 0) {
                        pq.add(node);
                    }
                }
                assert cnt == 1;
            }
            for (Node node : root.in) {
                decreaseOutDeg(node, 1);
            }
        }

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int m = in.ri();
            HashMap<Long, Node> nodes = new HashMap<>();
            for (int i = 0; i < m; i++) {
                int x = in.ri();
                int y = in.ri();
                Node node = new Node();
                node.id = i;
                long key = DigitUtils.asLong(x, y);
                nodes.put(key, node);
            }
            for (Map.Entry<Long, Node> entry : nodes.entrySet()) {
                int x = DigitUtils.highBit(entry.getKey());
                int y = DigitUtils.lowBit(entry.getKey());
                Node node = entry.getValue();
                for (int i = -1; i <= 1; i++) {
                    long key = DigitUtils.asLong(x + i, y - 1);
                    Node exist = nodes.get(key);
                    if (exist == null) {
                        continue;
                    }
                    node.out.add(exist);
                    node.outdeg++;
                    exist.in.add(node);
                }
                pq.add(node);
            }
            for (Node node : nodes.values()) {
                decreaseOutDeg(node, 0);
            }

            int mod = (int) 1e9 + 9;
            long sum = 0;
            boolean max = true;
            while (!pq.isEmpty()) {
                Node head = max ? pq.pollLast() : pq.pollFirst();
                debug.debug("head", head);
                sum = (sum * m + head.id) % mod;
                max = !max;
                removeNode(head);
            }
            out.println(sum);
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }

    static class Node {
        int id;
        List<Node> out = new ArrayList<>();
        List<Node> in = new ArrayList<>();
        int outdeg;
        int indeg;
        boolean removed;

        public String toString() {
            return "" + id;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 1 << 13;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int ri() {
            return readInt();
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class DigitUtils {
        public static long INT_TO_LONG_MASK = (1L << 32) - 1;

        private DigitUtils() {
        }

        public static long asLong(int high, int low) {
            return (((long) high) << 32) | (((long) low) & INT_TO_LONG_MASK);
        }

        public static int highBit(long x) {
            return (int) (x >> 32);
        }

        public static int lowBit(long x) {
            return (int) x;
        }

    }
}

