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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;

public class D {
	// author: Nagabhushan S Baddi

	// PRIMARY VARIABLES
	private static int n, m, k, x, y;
	private static int[] a, b;
	private static long ans;
	private static int[][] id, dp;
	private static int idf;
	private static String s, t;
	private static HashMap<Integer, ArrayList<Integer>> g;

	// CONSTANTS
	private static final long MOD = 998244353L;
	private static final int[] dx = { -1, 1, 0, 0 };
	private static final int[] dy = { 0, 0, -1, 1 };
	private static final int MAX = Integer.MAX_VALUE;
	private static final int MIN = Integer.MIN_VALUE;
	private static final long MAXLONG = (long) 1e18;
	private static final long MINLONG = -(long) 1e18;

	public static void main(String[] args) {
//		int testCases = in.nextInt();

		int m = (int) 1e6 + 10;
		boolean[] isPrime = new boolean[m];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] = false;
		
		int[] count = new int[m];
		Arrays.fill(count, 1);
		
		for(int i=2; i<m; i++) {
			if (isPrime[i]) {
				count[i] = 2;
				for(int j=2*i; j<m; j+=i) {
					isPrime[j] = false;
					count[j] *= get(j, i)+1;
				}
			}
		}

		n = ini();

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

		long dpSum = 0;
		dpSum += 1;

		for (int rem = 2; rem <= n; rem++) {
//			int count = 2 * rem;

//			for(int x=rem+1; x<=2*rem; x++) {
//				dp[rem] += dp[x-rem-1];
//				dp[rem] %= MOD;
//			}
			dp[rem] += dpSum;
			dp[rem] %= MOD;

//			int f = 0;
//			for (int x = 1; x * 1L * x <= rem; x++) {
//				if (rem % x == 0) {
//					if (x * 1L * x == rem) {
//						f++;
//					} else {
//						f += 2;
//					}
//				}
//			}
			dp[rem] += count[rem];
			dp[rem] %= MOD;

			dpSum += dp[rem];
			dpSum %= MOD;

//			pd(rem + " " + dp[rem]);
		}

		println(dp[n]);

		// f(n) = (f(n-1)) +

		// 1 2 3 4 5 6 7 8
		// n = 4

		// 1-4, 2-5, 3-6,

		// 1 -> diff+1
		// 2 -> diff+2
		// 3 -> diff+3
		// diff -> diff+diff

		// n = 2*diff or 4*diff or 6*diff
		// n = k*(2*diff)

		// 6 = 1*6, 2*3, 3*2, 6*1,

		out.flush();
		out.close();

	}

	private static int get(int x, int y) {
		int low = 1;
		int high = 22;
		
		while(low<=high) {
			int mid = (low+high)/2;
			int pow = (int)Math.pow(y, mid);
			
			int rem = x%pow;
			
			if (rem!=0) {
				high = mid-1;
			} else if (x%(pow*y)==0) {
				low = mid+1;
			} else {
				return mid;
			}
			
//			if (x%(int)Math.pow(y, mid)==0) {
//				return mid;
//			} else {
//				high = mid;
//			}
		}
		return 1;
	}
	
	// INIT
	private static void initCase(int z) {
		idf = z;
		ans = 0;
	}

	// PRINT ANSWER
	private static void printAns(Object o) {
		out.println(o);
	}

	private static void printAns(Object o, int testCaseNo) {
		out.println("Case #" + testCaseNo + ": " + o);
	}

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

	// SORT SHORTCUTS - QUICK SORT TO MERGE SORT
	private static void sort(int[] a) {
		int n = a.length;
		Integer[] b = new Integer[n];
		for (int i = 0; i < n; i++) {
			b[i] = a[i];
		}

		Arrays.sort(b);

		for (int i = 0; i < n; i++) {
			a[i] = b[i];
		}
	}

	private static void sort(long[] a) {
		int n = a.length;
		Long[] b = new Long[n];
		for (int i = 0; i < n; i++) {
			b[i] = a[i];
		}

		Arrays.sort(b);

		for (int i = 0; i < n; i++) {
			a[i] = b[i];
		}
	}

	// INPUT SHORTCUTS

	private static int[] ina(int n) {
		int[] temp = new int[n];
		for (int i = 0; i < n; i++) {
			temp[i] = in.nextInt();
		}
		return temp;
	}

	private static int[][] ina2d(int n, int m) {
		int[][] temp = new int[n][m];
		for (int i = 0; i < n; i++) {
			temp[i] = ina(m);
		}
		return temp;
	}

	private static char[][] ina2dChar(int n, int m) {
		char[][] temp = new char[n][];
		for (int i = 0; i < n; i++) {
			temp[i] = ins().toCharArray();
		}
		return temp;
	}

	private static int ini() {
		return in.nextInt();
	}

	private static long inl() {
		return in.nextLong();
	}

	private static double ind() {
		return Double.parseDouble(ins());
	}

	private static String ins() {
		return in.readString();
	}

	// PRINT SHORTCUTS
	private static void println(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
		out.write("\n");
	}

	private static void pd(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
		out.flush();
		out.write("\n");
	}

	private static void print(Object... o) {
		for (Object x : o) {
			out.write(x + "");
		}
	}

	// GRAPH SHORTCUTS
	private static HashMap<Integer, ArrayList<Integer>> intree(int n) {

		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();
		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < n - 1; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;
	}

	private static HashMap<Integer, ArrayList<Integer>> ingraph(int n, int m) {
		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
			g.get(v).add(u);
		}

		return g;

	}

	private static HashMap<Integer, ArrayList<Integer>> indirectedgraph(int n, int m) {
		HashMap<Integer, ArrayList<Integer>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			g.get(u).add(v);
		}

		return g;

	}

	private static HashMap<Integer, ArrayList<Edge>> inweightedgraph(int n, int m) {
		HashMap<Integer, ArrayList<Edge>> g = new HashMap<>();

		for (int i = 0; i < n; i++) {
			g.put(i, new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			int u = ini() - 1;
			int v = ini() - 1;
			int w = ini();
			Edge edge = new Edge(u, v, w);
			g.get(u).add(edge);
			g.get(v).add(edge);
		}

		return g;

	}

	private static class Edge implements Comparable<Edge> {
		private int u, v;
		private long w;

		public Edge(int a, int b, long c) {
			u = a;
			v = b;
			w = c;
		}

		public int other(int x) {
			return (x == u ? v : u);
		}

		public int compareTo(Edge edge) {
			return Long.compare(w, edge.w);
		}
	}

	private static class Pair {
		private int u, v;

		public Pair(int a, int b) {
			u = a;
			v = b;
		}

		public int hashCode() {
			return u + v + u * v;
		}

		public boolean equals(Object object) {
			Pair pair = (Pair) object;
			return u == pair.u && v == pair.v;
		}
	}

	private static class Triplet {
		private int u, v, w;

		public Triplet(int a, int b, int c) {
			u = a;
			v = b;
			w = c;
		}

		public int hashCode() {
			return u + v + w + u * v + v * w + u * w + u * v * w;
		}

		public boolean equals(Object object) {
			Triplet triplet = (Triplet) object;
			return u == triplet.u && v == triplet.v && v == triplet.w;
		}
	}

	private static class Node implements Comparable<Node> {
		private int u;
		private long dist;

		public Node(int a, long b) {
			u = a;
			dist = b;
		}

		public int compareTo(Node node) {
			return Long.compare(dist, node.dist);
		}
	}

	// MATHS AND NUMBER THEORY SHORTCUTS
	private static int gcd(int a, int b) {
		// O(log(min(a,b)))
		if (b == 0)
			return a;

		return gcd(b, a % b);
	}

	private static long modExp(long a, long b) {
		if (b == 0)
			return 1;

		a %= MOD;

		long exp = modExp(a, b / 2);

		if (b % 2 == 0) {
			return (exp * exp) % MOD;
		} else {
			return (a * ((exp * exp) % MOD)) % MOD;
		}
	}

	private static long mul(int a, int b) {
		return a * 1L * b;
	}

	// Segment Tree
	private static class SegmentTree<T extends Comparable<T>> {
		private int n, m;
		private T[] a;
		private T[] seg;
		private T NULLVALUE;

		public SegmentTree(int n, T NULLVALUE) {
			this.NULLVALUE = NULLVALUE;
			this.n = n;
			m = 4 * n;
			seg = (T[]) new Object[m];

		}

		public SegmentTree(T[] a, int n, T NULLVALUE) {
			this.NULLVALUE = NULLVALUE;
			this.a = a;
			this.n = n;
			m = 4 * n;
			seg = (T[]) new Object[m];
			construct(0, n - 1, 0);
		}

		private void update(int pos) {
			// Range Sum
			// seg[pos] = seg[2*pos+1]+seg[2*pos+2];

			// Range Min
			if (seg[2 * pos + 1].compareTo(seg[2 * pos + 2]) <= 0) {
				seg[pos] = seg[2 * pos + 1];
			} else {
				seg[pos] = seg[2 * pos + 2];
			}
		}

		private T optimum(T leftValue, T rightValue) {
			// Range Sum
			// return leftValue+rightValue;

			// Range Min
			if (leftValue.compareTo(rightValue) <= 0) {
				return leftValue;
			} else {
				return rightValue;
			}
		}

		public void construct(int low, int high, int pos) {
			if (low == high) {
				seg[pos] = a[low];
				return;
			}

			int mid = (low + high) / 2;

			construct(low, mid, 2 * pos + 1);
			construct(mid + 1, high, 2 * pos + 2);
			update(pos);
		}

		public void add(int index, T value) {
			add(index, value, 0, n - 1, 0);
		}

		private void add(int index, T value, int low, int high, int pos) {
			if (low == high) {
				seg[pos] = value;
				return;
			}

			int mid = (low + high) / 2;

			if (index <= mid) {
				add(index, value, low, mid, 2 * pos + 1);
			} else {
				add(index, value, mid + 1, high, 2 * pos + 2);
			}
			update(pos);
		}

		public T get(int qlow, int qhigh) {
			return get(qlow, qhigh, 0, n - 1, 0);
		}

		public T get(int qlow, int qhigh, int low, int high, int pos) {
			if (qlow > low || low > qhigh) {
				return NULLVALUE;
			} else if (qlow <= low || qhigh >= high) {
				return seg[pos];
			} else {
				int mid = (low + high) / 2;
				T leftValue = get(qlow, qhigh, low, mid, 2 * pos + 1);
				T rightValue = get(qlow, qhigh, mid + 1, high, 2 * pos + 2);

				return optimum(leftValue, rightValue);
			}
		}
	}

	// DSU
	private static class DSU {
		private int[] id;
		private int[] size;
		private int n;

		public DSU(int n) {
			this.n = n;

			id = new int[n];
			for (int i = 0; i < n; i++) {
				id[i] = i;
			}

			size = new int[n];
			Arrays.fill(size, 1);
		}

		private int root(int u) {
			while (u != id[u]) {
				id[u] = id[id[u]];
				u = id[u];
			}
			return u;
		}

		public boolean connected(int u, int v) {
			return root(u) == root(v);
		}

		public void union(int u, int v) {
			int p = root(u);
			int q = root(v);

			if (size[p] >= size[q]) {
				id[q] = p;
				size[p] += size[q];
			} else {
				id[p] = q;
				size[q] += size[p];
			}
		}
	}

	// KMP
	private static int countSearch(String s, String p) {
		int n = s.length();
		int m = p.length();

		int[] b = backTable(p);

		int j = 0;
		int count = 0;

		for (int i = 0; i < n; i++) {
			if (j == m) {
				j = b[j - 1];
				count++;
			}
			while (j != 0 && s.charAt(i) != p.charAt(j)) {
				j = b[j - 1];
			}
			if (s.charAt(i) == p.charAt(j)) {
				j++;
			}
		}

		if (j == m)
			count++;

		return count;
	}

	private static int[] backTable(String p) {
		int m = p.length();

		int j = 0;
		int[] b = new int[m];

		for (int i = 1; i < m; i++) {
			while (j != 0 && p.charAt(i) != p.charAt(j)) {
				j = b[j - 1];
			}
			if (p.charAt(i) == p.charAt(j)) {
				b[i] = ++j;
			}
		}
		return b;
	}

	private static int[][] countMap(String s) {
		int n = s.length();

		int[][] map = new int[n][26];

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < 26; j++) {
				map[i][j] = (i - 1 >= 0 ? map[i - 1][j] : 0);
			}
			map[i][s.charAt(i) - 'a']++;
		}

		return map;
	}

	private static int[][] rightOcc(String s) {
		int n = s.length();

		int[][] right = new int[n][26];

		for (int i = n - 1; i >= 0; i--) {
			for (int j = 0; j < 26; j++) {
				right[i][j] = (i + 1 < n ? right[i + 1][j] : -1);
			}
			right[i][s.charAt(i) - 'a'] = i;
		}

		return right;
	}

	private static int[][] leftOcc(String s) {
		int n = s.length();

		int[][] left = new int[n][26];

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < 26; j++) {
				left[i][j] = (i - 1 >= 0 ? left[i - 1][j] : -1);
			}
			left[i][s.charAt(i) - 'a'] = i;
		}

		return left;
	}

	// LCA
	private static class LCA {
		private HashMap<Integer, ArrayList<Integer>> g;
		private int[] level;
		private int[] a;
		private int[][] P;
		private int n, m;
		private int[] xor;

		public LCA(HashMap<Integer, ArrayList<Integer>> g, int[] a) {
			this.g = g;
			this.a = a;
			n = g.size();
			m = (int) (Math.log(n) / Math.log(2)) + 5;
			P = new int[n][m];
			xor = new int[n];
			level = new int[n];

			preprocess();
		}

		private void preprocess() {
			dfs(0, -1);

			for (int j = 1; j < m; j++) {
				for (int i = 0; i < n; i++) {
					if (P[i][j - 1] != -1) {
						P[i][j] = P[P[i][j - 1]][j - 1];
					}
				}
			}
		}

		private void dfs(int u, int p) {
			P[u][0] = p;
			xor[u] = a[u] ^ (p == -1 ? 0 : xor[p]);
			level[u] = (p == -1 ? 0 : level[p] + 1);

			for (int v : g.get(u)) {
				if (v == p)
					continue;
				dfs(v, u);
			}
		}

		public int lca(int u, int v) {
			if (level[v] > level[u]) {
				int temp = v;
				v = u;
				u = temp;
			}

			for (int j = m; j >= 0; j--) {
				if (level[u] - (1 << j) < level[v]) {
					continue;
				} else {
					u = P[u][j];
				}
			}

			if (u == v)
				return u;

			for (int j = m - 1; j >= 0; j--) {
				if (P[u][j] == -1 || P[u][j] == P[v][j]) {
					continue;
				} else {
					u = P[u][j];
					v = P[v][j];
				}
			}

			return P[u][0];
		}

		private int xor(int u, int v) {
			int l = lca(u, v);

			return xor[u] ^ xor[v] ^ a[l];
		}
	}

	// Geometry
	private static class Line {
		private int a, b, c;

		public Line(int x1, int y1, int x2, int y2) {
			a = y2 - y1;
			b = x1 - x2;
			c = a * x1 + b * y1;

			int g = gcd(a, gcd(b, c));

			a /= g;
			b /= g;
			c /= g;
		}

		public int hashCode() {
			return a + b + c + a * b + b * c + c * a + a * b * c;
		}

		public boolean equals(Object o) {
			Line line = (Line) o;
			return a == line.a && b == line.b && c == line.c;
		}
	}

	// FAST INPUT OUTPUT LIBRARY
	private static InputReader in = new InputReader(System.in);
	private static PrintWriter out = new PrintWriter(System.out);

	private static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;

		public InputReader(InputStream st) {
			this.stream = st;
		}

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}
}