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:
// Rohit Bohra | 24/05/2021 : 20:04:33
import java.io.*;
import java.util.*;

@SuppressWarnings("unchecked")
public class D{

    public static void main(String args[])throws IOException{
        
        int n=sc.nextInt();
        int[] dp = new int[n+1];
        dp[0]=1;
        for(int i=2;i<=n;i++){
            for(int j=i;j<=n;j+=i){
                dp[j]++;
            }
        }

        int pref=1;
        for(int i=1;i<=n;i++){
            // dp[i] = (dp[i]+dp[i-1])%M;
            dp[i]=(dp[i]+pref)%M;
            pref = (pref+dp[i])%M;
        }

        out.println(dp[n]);
        out.close();
    }
    

    static int M=998244353;

    public static void sort(int[] arr,boolean reverse){
        ArrayList<Integer> list = new ArrayList<Integer>();
        int n =arr.length;
        for(int i=0;i<n;i++){
            list.add(arr[i]);
        }

        if(reverse)
        Collections.sort(list,Collections.reverseOrder());
        else
        Collections.sort(list);

        for(int i=0;i<n;i++){
            arr[i] = list.get(i);
        }
    }

    public static double min(double ...a){
        double min=Double.MAX_VALUE;
        for(double i : a)
        min =Math.min(i,min);
        return min;
    }

    public static long min(long ...a){
        long min=Long.MAX_VALUE;
        for(long i : a)
        min =Math.min(i,min);
        return min;
    }

    public static int min(int ...a){
        int min=Integer.MAX_VALUE;
        for(int i : a)
        min =Math.min(i,min);
        return min;
    }

    public static double max(double ...a){
        double max=Double.MIN_VALUE;
        for(double i : a)
        max =Math.max(i,max);
        return max;
    }

    public static long max(long ...a){
        long max=Long.MIN_VALUE;
        for(long i : a)
        max =Math.max(i,max);
        return max;
    }

    public static int max(int ...a){
        int max=Integer.MIN_VALUE;
        for(int i : a)
        max =Math.max(i,max);
        return max;
    }

    public static long pow(long a,long b){
        long res=1;
        while(b>0){
            if((b&1)==1)
                res = res*a;
            a=a*a;
            b >>= 1;
        }
        return res;
    }

    public static long pow(long a,long b,long m){
        a%=m;
        long res=1;
        while(b>0){
            if((b&1)==1)
                res = (res*a)%m;
            a=(a*a)%m;
            b >>= 1;
        }
        return res;
    }

    public static int gcd(int a,int b){
        if(b==0) return a;
        return gcd(b,a%b);
    }

    static class Pair{

        // Implementing equals() and hashCode()
        // Map<Pair, V> map = //...

        private final int x;
        private final int y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair pair = (Pair) o;
            return x == pair.x && y == pair.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
    }

    static FastScanner sc = new FastScanner();
    static PrintWriter out =new PrintWriter(System.out);

    static class FastScanner {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st=new StringTokenizer("");
            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st=new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }
            
            int nextInt() {
                return Integer.parseInt(next());
            }
            int[] readArray(int n) {
                int[] a=new int[n];
                for (int i=0; i<n; i++) a[i]=nextInt();
                return a;
            }
            long nextLong() {
                return Long.parseLong(next());
            }
            float nextFloat() {
                return Float.parseFloat(next());
            }
            double nextDouble() {
                return Double.parseDouble(next());
            }
            public long[] readLongArray(int n) {
                long[] a=new long[n];
                for (int i=0; i<n; i++) a[i]=nextLong();
                return a;
            }
            public double[] readDoubleArray(int n) {
                double[] a=new double[n];
                for (int i=0; i<n; i++) a[i]=nextDouble();
                return a;
            }
    }
}