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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;

public class Solution {
  private static int readInt() throws Exception {
    return Integer.parseInt(br.readLine());
  }

  private static long readLong() throws Exception {
    return Long.parseLong(br.readLine());
  }

  public static int[] readIntArray() throws Exception {
    String line = br.readLine();
    if (line == null || line.isEmpty()) return null;
    String[] lines = line.split(" ");
    int n = Integer.parseInt(lines[0]);
    int[] nums = new int[n];
    for (int i = 0; i < n; i++)
      nums[i] = Integer.parseInt(lines[i + 1]);
    return nums;
  }

  public static int[] readIntArray(int n) throws Exception {
    int[] nums = new int[n];
    String[] lines = br.readLine().split(" ");
    for (int i = 0; i < n; i++)
      nums[i] = Integer.parseInt(lines[i]);
    return nums;
  }

  public static long[] readLongArray(int n) throws Exception {
    long[] nums = new long[n];
    String[] lines = br.readLine().split(" ");
    for (int i = 0; i < n; i++)
      nums[i] = Long.parseLong(lines[i]);
    return nums;
  }

  public static String[] readStringArray(int n) throws Exception {
    String[] nums = new String[n];
    for (int i = 0; i < n; i++)
      nums[i] = br.readLine();
    return nums;
  }

  public static void printArrayInline(int[] nums) throws Exception {
    for (int i = 0; i < nums.length - 1; i++) {
      bw.write(nums[i] + " ");
    }
    bw.write(nums[nums.length - 1] + "\n");
  }

  public static void printArrayInline(long[] nums) throws Exception {
    for (int i = 0; i < nums.length - 1; i++) {
      bw.write(nums[i] + " ");
    }
    bw.write(nums[nums.length - 1] + "\n");
  }

  public static <T> void printListInLine(List<T> nums) throws Exception {
    for (int i = 0; i < nums.size() - 1; i++) {
      bw.write(nums.get(i).toString() + " ");
    }
    bw.write(nums.get(nums.size() - 1) + "\n");
  }

  public static <T> void printListMultiLine(List<T> nums) throws Exception {
    for (T num : nums) {
      bw.write(num.toString() + "\n");
    }
  }

  public static void printArrayMultiLine(int[] nums) throws Exception {
    for (int num : nums) {
      bw.write(num + "\n");
    }
  }

  public static int[] makeRandomArray(int size, int lower, int upper) {
    Random random = new Random(System.currentTimeMillis());
    int[] nums = new int[size];
    for (int i = 0; i < size; i++)
      nums[i] = random.nextInt(upper - lower + 1) + lower;
    return nums;
  }

  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static PrintWriter bw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
//  static {
//    try {
//      String env = System.getProperty("env-jay");
//      if (env != null && env.equals("jay")) {
//        br = new BufferedReader(new FileReader("src/input.txt"));
//        bw = new PrintWriter(new BufferedWriter(new FileWriter("src/output.txt", false)));
//      }
//    } catch (Throwable e) {
//
//    }
//  }
//
//
//  private static void test() throws Exception {
//    try {
//      String env = System.getProperty("env-jay");
//      if (env != null && env.equals("jay")) {
//        var output = new BufferedReader(new FileReader("src/output.txt"));
//        var expected = new BufferedReader(new FileReader("src/expected.txt"));
//        String ans;
//        int line = 0;
//        while ((ans = expected.readLine()) != null && !ans.isEmpty()) {
//          line++;
//          String guess = output.readLine();
//          if (guess == null || guess.isEmpty()) {
//            System.err.println(String.format(
//                    "Line[%d] There is no guess.\nAnswer:[%s]"
//                    , line, ans));
//            System.exit(-1);
//          }
//          if (!ans.equals(guess)) {
//            System.err.println(String.format(
//                    "Line[%d], Wrong guess.\nAnswer:[%s]\nGuess:[%s]"
//                    , line, ans, guess));
//            System.exit(-2);
//          }
//        }
//      }
//    } catch (Throwable e) {
//
//    }
//  }

  public static void main(String[] args) throws Exception {
    int testCases = 1;
    for (int iter = 1; iter <= testCases; iter++) {
      bw.printf("%d\n", solve(readInt()));
    }
    bw.flush();
    bw.close();
    br.close();
    //test();
  }
  static long mod = 998244353;
  private static long solve(int n) {
    long[] memo = new long[1000001];
    long[] factors = factor(2 * n);
    memo[1] = 1;
    long sum = 0;
    for(int i = 2; i <= n; i ++) {
      long factor = factors[i] % mod;
      sum = (sum + memo[i-1]) % mod;
      memo[i] = (sum + factor) % mod;
    }
    return memo[n];
  }
  private static long[] factor(int n) {
    long[] factors = new long[n + 50];
    for(int i=1; i < n; i++){
      for(int j=1; j < n/i; j++){
        factors[i*j]++;
      }
    }
    return factors;
  }
}