Problem: Consider a square grid with h rows and w columns with some dominoes on it. Each domino covers exactly two cells of the grid that share a common side. Every cell is covered by at most one domino.

Let's call a placement of dominoes on the grid perfectly balanced if no row and no column contains a pair of cells covered by two different dominoes. In other words, every row and column may contain no covered cells, one covered cell, or two covered cells that belong to the same domino.

You are given a perfectly balanced placement of dominoes on a grid. Find the number of ways to place zero or more extra dominoes on this grid to keep the placement perfectly balanced. Output this number modulo 998 244 353.

Input

The first line contains three integers h, w, and n (1 ≤ h, w ≤ 3600; 0 ≤ n ≤ 2400), denoting the dimensions of the grid and the number of already placed dominoes. The rows are numbered from 1 to h, and the columns are numbered from 1 to w.

Each of the next n lines contains four integers r_{i, 1}, c_{i, 1}, r_{i, 2}, c_{i, 2} (1 ≤ r_{i, 1} ≤ r_{i, 2} ≤ h; 1 ≤ c_{i, 1} ≤ c_{i, 2} ≤ w), denoting the row id and the column id of the cells covered by the i-th domino. Cells (r_{i, 1}, c_{i, 1}) and (r_{i, 2}, c_{i, 2}) are distinct and share a common side.

The given domino placement is perfectly balanced.

Output

Output the number of ways to place zero or more extra dominoes on the grid to keep the placement perfectly balanced, modulo 998 244 353.

Examples

Input


5 7 2
3 1 3 2
4 4 4 5


Output


8


Input


5 4 2
1 2 2 2
4 3 4 4


Output


1


Input


23 42 0


Output


102848351

Note

In the first example, the initial grid looks like this:

<image>

Here are 8 ways to place zero or more extra dominoes to keep the placement perfectly balanced:

<image>

In the second example, the initial grid looks like this:

<image>

No extra dominoes can be placed here.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
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);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int h = in.readInt();
            int w = in.readInt();
            int n = in.readInt();
            int[] r = new int[2 * n];
            int[] c = new int[2 * n];
            in.readIntArrays(r, c);
            MiscUtils.decreaseByOne(r, c);
            ArrayUtils.sort(r);
            r = ArrayUtils.unique(r);
            ArrayUtils.sort(c);
            c = ArrayUtils.unique(c);
            long[] horizontal = go(c, w);
            long[] vertical = go(r, h);
            long[] fact = IntegerUtils.generateFactorial(Math.max(h, w) + 1, MiscUtils.MODF);
            long[] rev = IntegerUtils.generateReverseFactorials(Math.max(h, w) + 1, MiscUtils.MODF);
            long answer = 0;
            for (int i = 0; i < horizontal.length; i++) {
                for (int j = 0; j < vertical.length; j++) {
                    if (2 * i + j <= w - c.length && 2 * j + i <= h - r.length) {
                        answer += horizontal[i] * vertical[j] % MiscUtils.MODF * fact[h - r.length - 2 * j] %
                                MiscUtils.MODF * rev[h - r.length - 2 * j - i] % MiscUtils.MODF
                                * fact[w - c.length - 2 * i] % MiscUtils.MODF * rev[w - c.length - 2 * i - j] %
                                MiscUtils.MODF;
                    }
                }
            }
            out.printLine(answer % MiscUtils.MODF);
        }

        private long[] go(int[] c, int w) {
            long[] result = new long[(w - c.length) / 2 + 1];
            long[] next = new long[result.length];
            long[] last = new long[result.length];
            result[0] = 1;
            int at = c.length - 1;
            int col = w;
            for (int i = w - 1; i >= 0; i--) {
                System.arraycopy(result, 0, next, 0, result.length);
                if (at >= 0 && c[at] == i) {
                    col = i;
                    at--;
                }
                if (col >= i + 2) {
                    for (int j = 1; j < result.length; j++) {
                        next[j] += last[j - 1];
                        if (next[j] >= MiscUtils.MODF) {
                            next[j] -= MiscUtils.MODF;
                        }
                    }
                }
                long[] temp = last;
                last = result;
                result = next;
                next = temp;
            }
            return result;
        }

    }

    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 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 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 ArrayUtils {
        public static int[] sort(int[] array) {
            return sort(array, IntComparator.DEFAULT);
        }

        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[] unique(int[] array) {
            return new IntArray(array).unique().toArray();
        }

    }

    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 interface IntReversableCollection extends IntCollection {
    }

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

        public int compare(int first, int second);

    }

    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 IntList unique() {
            int last = Integer.MIN_VALUE;
            IntList result = new IntArrayList();
            int size = size();
            for (int i = 0; i < size; i++) {
                int current = get(i);
                if (current != last) {
                    result.add(current);
                    last = current;
                }
            }
            return result;
        }

        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 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 interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    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;
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

    }

    static class IntegerUtils {
        public static long[] generateFactorial(int count, long module) {
            long[] result = new long[count];
            if (module == -1) {
                if (count != 0) {
                    result[0] = 1;
                }
                for (int i = 1; i < count; i++) {
                    result[i] = result[i - 1] * i;
                }
            } else {
                if (count != 0) {
                    result[0] = 1 % module;
                }
                for (int i = 1; i < count; i++) {
                    result[i] = (result[i - 1] * i) % module;
                }
            }
            return result;
        }

        public static long[] generateReverse(int upTo, long module) {
            long[] result = new long[upTo];
            if (upTo > 1) {
                result[1] = 1;
            }
            for (int i = 2; i < upTo; i++) {
                result[i] = (module - module / i * result[((int) (module % i))] % module) % module;
            }
            return result;
        }

        public static long[] generateReverseFactorials(int upTo, long module) {
            long[] result = generateReverse(upTo, module);
            if (upTo > 0) {
                result[0] = 1;
            }
            for (int i = 1; i < upTo; i++) {
                result[i] = result[i] * result[i - 1] % module;
            }
            return result;
        }

    }

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

        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 class MiscUtils {
        public static final int MODF = 998_244_353;

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

    }
}