This is the second subtask of problem F. The only differences between this and the first subtask are the constraints on the value of m and the time limit. It is sufficient to solve this subtask in order to hack it, but you need to solve both subtasks in order to hack the first one.

There are n+1 distinct colours in the universe, numbered 0 through n. There is a strip of paper m centimetres long initially painted with colour 0. 

Alice took a brush and painted the strip using the following process. For each i from 1 to n, in this order, she picks two integers 0 ≤ a_i < b_i ≤ m, such that the segment [a_i, b_i] is currently painted with a single colour, and repaints it with colour i. 

Alice chose the segments in such a way that each centimetre is now painted in some colour other than 0. Formally, the segment [i-1, i] is painted with colour c_i (c_i ≠ 0). Every colour other than 0 is visible on the strip.

Count the number of different pairs of sequences \\{a_i\}_{i=1}^n, \\{b_i\}_{i=1}^n that result in this configuration. 

Since this number may be large, output it modulo 998244353.

Input

The first line contains a two integers n, m (1 ≤ n ≤ 500, n ≤ m ≤ 10^6) — the number of colours excluding the colour 0 and the length of the paper, respectively.

The second line contains m space separated integers c_1, c_2, …, c_m (1 ≤ c_i ≤ n) — the colour visible on the segment [i-1, i] after the process ends. It is guaranteed that for all j between 1 and n there is an index k such that c_k = j.

Output

Output a single integer — the number of ways Alice can perform the painting, modulo 998244353.

Examples

Input


3 3
1 2 3


Output


5


Input


2 3
1 2 1


Output


1


Input


2 3
2 1 2


Output


0


Input


7 7
4 5 1 6 2 3 7


Output


165


Input


8 17
1 3 2 2 7 8 2 5 5 4 4 4 1 1 6 1 1


Output


20

Note

In the first example, there are 5 ways, all depicted in the figure below. Here, 0 is white, 1 is red, 2 is green and 3 is blue.

<image>

Below is an example of a painting process that is not valid, as in the second step the segment 1 3 is not single colour, and thus may not be repainted with colour 2.

<image>

In the second example, Alice must first paint segment 0 3 with colour 1 and then segment 1 2 with colour 2. 
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);
        TaskF2 solver = new TaskF2();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF2 {
        long[][] result;
        long[][] split;
        int[] c;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int m = in.readInt();
            int[] c = in.readIntArray(m);
            MiscUtils.decreaseByOne(c);
            int[] min = new int[n];
            int[] max = new int[n];
            Arrays.fill(min, m - 1);
            for (int i = 0; i < m; i++) {
                min[c[i]] = Math.min(min[c[i]], i);
                max[c[i]] = Math.max(max[c[i]], i);
            }
            result = new long[n][n];
            split = new long[n][n];
            long answer = 1;
            for (int i = n - 1; i >= 0; i--) {
                for (int j = min[i]; j <= max[i]; j++) {
                    if (c[j] != i) {
                        IntList colors = new IntArrayList();
                        while (c[j] != i) {
                            if (c[j] < i) {
                                out.printLine(0);
                                return;
                            }
                            colors.add(c[j]);
                            j = max[c[j]] + 1;
                        }
                        answer *= solve(colors.toArray());
                        answer %= MiscUtils.MODF;
                    }
                }
            }
            IntList colors = new IntArrayList();
            int j = 0;
            while (j < m) {
                colors.add(c[j]);
                j = max[c[j]] + 1;
            }
            answer *= solve(colors.toArray());
            answer %= MiscUtils.MODF;
            out.printLine(answer);
        }

        private long solve(int[] c) {
            this.c = c;
            int nn = c.length;
            for (int i = 0; i < nn; i++) {
                Arrays.fill(result[i], 0, nn, -1);
                Arrays.fill(split[i], 0, nn, -1);
            }
            return go(0, nn - 1);
        }

        private long go(int f, int t) {
            if (f >= t) {
                return 1;
            }
            if (result[f][t] != -1) {
                return result[f][t];
            }
            int at = f;
            for (int j = f + 1; j <= t; j++) {
                if (c[j] < c[at]) {
                    at = j;
                }
            }
            return result[f][t] = goSplit(f, at - 1) * goSplit(at + 1, t) % MiscUtils.MODF;
        }

        private long goSplit(int f, int t) {
            if (f > t) {
                return 1;
            }
            if (split[f][t] != -1) {
                return split[f][t];
            }
            split[f][t] = 0;
            for (int i = f - 1; i <= t; i++) {
                split[f][t] += go(f, i) * go(i + 1, t) % MiscUtils.MODF;
            }
            return split[f][t] %= MiscUtils.MODF;
        }

    }

    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]--;
                }
            }
        }

    }

    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 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 interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

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

    }

    static interface IntReversableCollection extends IntCollection {
    }

    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);
        }

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

    }

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

        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);

        }

    }
}

