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.io.*;
import java.util.*;

public class D implements Runnable {

   int[] divisors;

   void solve() throws IOException {
      int n = ri();
      divisors = new int[n + 1];
      mod = 998244353;

      preCompute();

      long prev = 1;
      long[] dp = lArr(n + 1);
      dp[0] = dp[1] = 1;
      for (int i = 2; i <= n; i++) {
         dp[i] = divisors[i];
         dp[i] = add(dp[i], prev);
         prev = add(prev, dp[i]);
      }
      println(dp[n]);
   }

   long add(long a, long b) {
      return (a + b) % mod;
   }

   void preCompute() {

      for (int i = 1; i < divisors.length; i++) {
         for (int j = i; j < divisors.length; j += i) {
            divisors[j]++;
         }
      }
   }

   /************************************************************************************************************************************************/
   public static void main(String[] args) throws IOException {
      new Thread(null, new D(), "1").start();
   }

   static PrintWriter out = new PrintWriter(System.out);
   static Reader read = new Reader();
   static StringBuilder sbr = new StringBuilder();
   static int mod = (int) 1e9 + 7;
   static int dmax = Integer.MAX_VALUE;
   static long lmax = Long.MAX_VALUE;
   static int dmin = Integer.MIN_VALUE;
   static long lmin = Long.MIN_VALUE;

   @Override
   public void run() {
      try {
         solve();
         out.close();
      } catch (IOException e) {
         e.printStackTrace();
         System.exit(1);
      }
   }

   static class Reader {
      private byte[] buf = new byte[1024];
      private int index;
      private InputStream in;
      private int total;

      public Reader() {
         in = System.in;
      }

      public int scan() throws IOException {
         if (total < 0)
            throw new InputMismatchException();
         if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
               return -1;
         }
         return buf[index++];
      }

      public int intNext() throws IOException {
         int integer = 0;
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         int neg = 1;
         if (n == '-') {
            neg = -1;
            n = scan();
         }
         while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
               integer *= 10;
               integer += n - '0';
               n = scan();
            } else
               throw new InputMismatchException();
         }
         return neg * integer;
      }

      public double doubleNext() throws IOException {
         double doub = 0;
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         int neg = 1;
         if (n == '-') {
            neg = -1;
            n = scan();
         }
         while (!isWhiteSpace(n) && n != '.') {
            if (n >= '0' && n <= '9') {
               doub *= 10;
               doub += n - '0';
               n = scan();
            } else
               throw new InputMismatchException();
         }
         if (n == '.') {
            n = scan();
            double temp = 1;
            while (!isWhiteSpace(n)) {
               if (n >= '0' && n <= '9') {
                  temp /= 10;
                  doub += (n - '0') * temp;
                  n = scan();
               } else
                  throw new InputMismatchException();
            }
         }
         return doub * neg;
      }

      public String read() throws IOException {
         StringBuilder sb = new StringBuilder();
         int n = scan();
         while (isWhiteSpace(n))
            n = scan();
         while (!isWhiteSpace(n)) {
            sb.append((char) n);
            n = scan();
         }
         return sb.toString();
      }

      private boolean isWhiteSpace(int n) {
         if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
            return true;
         return false;
      }
   }

   static void shuffle(int[] aa) {
      int n = aa.length;
      Random rand = new Random();
      for (int i = 1; i < n; i++) {
         int j = rand.nextInt(i + 1);
         int tmp = aa[i];
         aa[i] = aa[j];
         aa[j] = tmp;
      }
   }

   static void shuffle(int[][] aa) {
      int n = aa.length;
      Random rand = new Random();
      for (int i = 1; i < n; i++) {
         int j = rand.nextInt(i + 1);
         int first = aa[i][0];
         int second = aa[i][1];
         aa[i][0] = aa[j][0];
         aa[i][1] = aa[j][1];
         aa[j][0] = first;
         aa[j][1] = second;
      }
   }

   // Gives strict lowerBound that previous number would be smaller than the target
   int lowerBound(int[] arr, int val) {
      int l = 0, r = arr.length - 1;
      while (l < r) {
         int mid = (r + l) >> 1;
         if (arr[mid] >= val) {
            r = mid;
         } else
            l = mid + 1;
      }
      return l;
   }

   // Gives strict upperBound that next number would be greater than the target
   int upperBound(int[] arr, int val) {
      int l = 0, r = arr.length - 1;
      while (l < r) {
         int mid = (r + l + 1) >> 1;
         if (arr[mid] <= val) {
            l = mid;
         } else
            r = mid - 1;
      }
      return l;
   }

   static void print(Object object) {
      out.print(object);
   }

   static void println(Object object) {
      out.println(object);
   }

   static int[] iArr(int len) {
      return new int[len];
   }

   static long[] lArr(int len) {
      return new long[len];
   }

   static long min(long a, long b) {
      return Math.min(a, b);
   }

   static int min(int a, int b) {
      return Math.min(a, b);
   }

   static long max(Long a, Long b) {
      return Math.max(a, b);
   }

   static int max(int a, int b) {
      return Math.max(a, b);
   }

   static int ri() throws IOException {
      return read.intNext();
   }

   static long rl() throws IOException {
      return Long.parseLong(read.read());
   }

   static String rs() throws IOException {
      return read.read();
   }

   static char rc() throws IOException {
      return rs().charAt(0);
   }

   static double rd() throws IOException {
      return read.doubleNext();
   }
}