Problem: Kavi has 2n points lying on the OX axis, i-th of which is located at x = i.

Kavi considers all ways to split these 2n points into n pairs. Among those, he is interested in good pairings, which are defined as follows:

Consider n segments with ends at the points in correspondent pairs. The pairing is called good, if for every 2 different segments A and B among those, at least one of the following holds:

  * One of the segments A and B lies completely inside the other. 
  * A and B have the same length. 



Consider the following example:

<image>

A is a good pairing since the red segment lies completely inside the blue segment.

B is a good pairing since the red and the blue segment have the same length.

C is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.

Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo 998244353.

Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

Input

The single line of the input contains a single integer n (1≤ n ≤ 10^6).

Output

Print the number of good pairings modulo 998244353.

Examples

Input


1


Output


1

Input


2


Output


3

Input


3


Output


6

Input


100


Output


688750769

Note

The good pairings for the second example are: 

<image>

In the third example, the good pairings are: 

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class D {

    public void prayGod() throws IOException {
        int n = nextInt();

        if (n == 1) {
            out.println(1);
            return;
        }

        long[] dp = new long[n + 1];
        dp[0] = 1;

        for (int i = 1; i <= n; i++) {
            for (int j = i * 2; j <= n; j += i)
                dp[j] = (dp[j] + 1) % mod;
        }

        long pref = 1;
        for (int i = 1; i <= n; i++) {
            dp[i] = (dp[i] + pref) % mod;
            pref = (pref + dp[i]) % mod;
        }

        out.println(dp[n]);

    }

    static final boolean RUN_TIMING = true;
    static final boolean AUTOFLUSH = false;
    static final boolean FILE_INPUT = false;
    static final boolean FILE_OUTPUT = false;

    static int iinf = 0x3f3f3f3f;
    static long inf = (long) 1e18 + 10;
    static long mod = 998244353L;

    static char[] inputBuffer = new char[1 << 20];
    static PushbackReader in = new PushbackReader(new BufferedReader(new InputStreamReader(System.in)), 1 << 20);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), AUTOFLUSH);

    // int data-type
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    public void sort(int[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    public static void printArray(int[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    // long data-type
    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

    public static void printArray(long[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    public void sort(long[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    // double data-type
    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) throws IOException {
        double[] arr = new double[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextDouble();
        return arr;
    }

    public static void printArray(double[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    // Generic type
    public <T> void sort(T[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    public static <T> void printArray(T[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    public String next() throws IOException {
        int len = 0;
        int c;
        do {
            c = in.read();
        } while (Character.isWhitespace(c) && c != -1);
        if (c == -1) {
            throw new NoSuchElementException("Reached EOF");
        }
        do {
            inputBuffer[len] = (char) c;
            len++;
            c = in.read();
        } while (!Character.isWhitespace(c) && c != -1);
        while (c != '\n' && Character.isWhitespace(c) && c != -1) {
            c = in.read();
        }
        if (c != -1 && c != '\n') {
            in.unread(c);
        }
        return new String(inputBuffer, 0, len);
    }

    public String nextLine() throws IOException {
        int len = 0;
        int c;
        while ((c = in.read()) != '\n' && c != -1) {
            if (c == '\r') {
                continue;
            }
            inputBuffer[len] = (char) c;
            len++;
        }
        return new String(inputBuffer, 0, len);
    }

    public boolean hasNext() throws IOException {
        String line = nextLine();
        if (line.isEmpty()) {
            return false;
        }
        in.unread('\n');
        in.unread(line.toCharArray());
        return true;
    }

    public void shuffle(int[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(long[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(Object[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            Object temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public static void main(String[] args) throws IOException {
        if (FILE_INPUT)
            in = new PushbackReader(new BufferedReader(new FileReader(new File("output.txt"))), 1 << 20);
        if (FILE_OUTPUT)
            out = new PrintWriter(new FileWriter(new File("output.txt")));

        long time = 0;
        time -= System.nanoTime();
        new D().prayGod();
        time += System.nanoTime();

        if (RUN_TIMING)
            System.err.printf("%.3f ms%n", time / 1000000.0);

        out.flush();
        in.close();
    }
}