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.*;
import java.math.BigInteger;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static long mod = 998244353;
	static long inf = (long) 1e16;
	static int n, m, k;
	static ArrayList<Integer>[] ad;
	static int[][] remove, add;
	static long[][] memo;
	static boolean vis[];
	static long[] inv, ncr[];
	static HashMap<Integer, Integer> hm;
	static int[] pre, suf, Smax[], Smin[];
	static int idmax, idmin;
	static ArrayList<Integer> av;
	static HashMap<Integer, Integer> mm;
	static boolean[] msks;
	static int[] lazy[], lazyCount;
	static int[] dist;
	static int[] g;
	static int st, ed;
	static ArrayList<Integer> gl;
	static int[] a, r;
	static int ans;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n = sc.nextInt();
		long[] f = new long[n + 1];
		f[1] = 1;
		int[] div = new int[n + 1];
		for (int i = 1; i <= n; i++) {
			for (int j = i; j <= n; j += i)
				div[j]++;
		}
		long sum = 1;
	//	System.out.println(Arrays.toString(div));
		for (int i = 2; i <= n; i++) {
			f[i] = sum + div[i];
			if (f[i] >= mod)
				f[i] -= mod;
			sum += f[i];
			if (sum >= mod)
				sum -= mod;
		}
	//	System.out.println(Arrays.toString(f));
		System.out.println(f[n]);
		out.flush();
	}

	static void compelete(int num) {
		if (num > n) {
			int[] len = new int[n + 1];
			int[] l = new int[n + 1];
			int[] r = new int[n + 1];
			Arrays.fill(l, -1);
			for (int i = 0; i < a.length; i++) {
				int x = a[i];
				if (l[x] == -1) {
					l[x] = i;
				} else {
					r[x] = i;
					len[x] = i - l[x];
				}
			}
			for (int i = 1; i <= n; i++)
				for (int j = i + 1; j <= n; j++) {
					int c = 0;
					if (len[i] != len[j])
						c++;
					if (!(l[i] <= l[j] && r[i] >= r[j]))
						c++;
					if (!(l[j] <= l[i] && r[j] >= r[i]))
						c++;
					if (c == 3)
						return;
				}
			ans++;
			return;
		}
		int st = 0;
		for (int i = 0; i < a.length; i++)
			if (a[i] == 0) {
				st = i;
				break;
			}
		for (int i = st + 1; i < a.length; i++) {
			if (a[i] == 0) {
				a[st] = num;
				a[i] = num;
				compelete(num + 1);
				a[st] = 0;
				a[i] = 0;
			}
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

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

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

		public int[] nextArrIntSorted(int n) throws IOException {
			int[] a = new int[n];
			Integer[] a1 = new Integer[n];
			for (int i = 0; i < n; i++)
				a1[i] = nextInt();
			Arrays.sort(a1);
			for (int i = 0; i < n; i++)
				a[i] = a1[i].intValue();
			return a;
		}

		public long[] nextArrLongSorted(int n) throws IOException {
			long[] a = new long[n];
			Long[] a1 = new Long[n];
			for (int i = 0; i < n; i++)
				a1[i] = nextLong();
			Arrays.sort(a1);
			for (int i = 0; i < n; i++)
				a[i] = a1[i].longValue();
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}