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:
public class Main {

	public static void main(String[] args) {
		new Main();
	}

	public Main() {
		FastScanner fs = new FastScanner();
		java.io.PrintWriter out = new java.io.PrintWriter(System.out);
		solve(fs, out);
		out.flush();
	}

	public void solve(FastScanner fs, java.io.PrintWriter out) {
		int n = fs.nextInt();
		int[] dp = new int[n + 1];
		int sum = 0;
		for (int i = 1;i <= n;++ i) {
			for (int j = i;j <= n;j += i) ++ dp[j];
			dp[i] += sum;
			dp[i] %= 998244353;
			sum += dp[i];
			sum %= 998244353;
		}
		out.println(dp[n]);
	}
}

class FastScanner {

	private final java.io.InputStream in = System.in;
	private final byte[] buffer = new byte[8192];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) return true;
		ptr = 0;
		try {
			buflen = in.read(buffer);
		} catch (java.io.IOException e) {
			e.printStackTrace();
		}
		return buflen > 0;
	}

	private byte readByte() {
		return hasNextByte() ? buffer[ptr++ ] : -1;
	}

	private static boolean isPrintableChar(byte c) {
		return 32 < c || c < 0;
	}

	private static boolean isNumber(int c) {
		return '0' <= c && c <= '9';
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++ ;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		byte b;
		while (isPrintableChar(b = readByte()))
			sb.appendCodePoint(b);
		return sb.toString();
	}

	public final char nextChar() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		return (char)readByte();
	}

	public final long nextLong() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		long n = 0;
		try {
			byte b = readByte();
			if (b == '-') {
				while (isNumber(b = readByte()))
					n = n * 10 + '0' - b;
				return n;
			} else if (!isNumber(b)) throw new NumberFormatException();
			do
				n = n * 10 + b - '0';
			while (isNumber(b = readByte()));
		} catch (java.util.NoSuchElementException e) {}
		return n;
	}

	public final int nextInt() {
		if (!hasNext()) throw new java.util.NoSuchElementException();
		int n = 0;
		try {
			byte b = readByte();
			if (b == '-') {
				while (isNumber(b = readByte()))
					n = n * 10 + '0' - b;
				return n;
			} else if (!isNumber(b)) throw new NumberFormatException();
			do
				n = n * 10 + b - '0';
			while (isNumber(b = readByte()));
		} catch (java.util.NoSuchElementException e) {}
		return n;
	}

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

class Arrays {

	public static void sort(final int[] array) {
		int l, min = 0xFFFFFFFF, max = 0;
		for (l = 0; l < array.length; ++l) {
			int i = array[l];
			min &= i;
			max |= i;
			if ((i & 0x80000000) == 0) break;
		}
		for (int r = l + 1; r < array.length; ++r) {
			int i = array[r];
			min &= i;
			max |= i;
			if ((i & 0x80000000) != 0) {
				array[r] = array[l];
				array[l++ ] = i;
			}
		}
		int use = min ^ max, bit = Integer.highestOneBit(use & 0x7FFFFFFF);
		if (bit == 0) return;
		sort(array, 0, l, use, bit);
		sort(array, l, array.length, use, bit);
	}

	private static void sort(final int[] array, final int left, final int right, final int use, int digit) {
		if (right - left <= 96) {
			for (int i = left + 1; i < right; ++i) {
				int tmp = array[i], tmp2, j;
				for (j = i; j > left && (tmp2 = array[j - 1]) > tmp; --j)
					array[j] = tmp2;
				array[j] = tmp;
			}
			return;
		}
		int l = left;
		while (l < right && (array[l] & digit) == 0)
			++l;
		for (int r = l + 1; r < right; ++r) {
			int i = array[r];
			if ((i & digit) == 0) {
				array[r] = array[l];
				array[l++ ] = i;
			}
		}
		if ((digit = Integer.highestOneBit(use & digit - 1)) == 0) return;
		sort(array, left, l, use, digit);
		sort(array, l, right, use, digit);
	}

	public static void sort(final long[] array) {
		int l;
		long min = 0xFFFFFFFFFFFFFFFFL, max = 0;
		for (l = 0; l < array.length; ++l) {
			long i = array[l];
			min &= i;
			max |= i;
			if ((i & 0x8000000000000000L) == 0) break;
		}
		for (int r = l + 1; r < array.length; ++r) {
			long i = array[r];
			min &= i;
			max |= i;
			if ((i & 0x8000000000000000L) != 0) {
				array[r] = array[l];
				array[l++ ] = i;
			}
		}
		long use = min ^ max, bit = Long.highestOneBit(use & 0x7FFFFFFFFFFFFFFFL);
		if (bit == 0) return;
		sort(array, 0, l, use, bit);
		sort(array, l, array.length, use, bit);
	}

	private static void sort(final long[] array, final int left, final int right, final long use, long digit) {
		if (right - left <= 96) {
			for (int i = left + 1, j; i < right; ++i) {
				long tmp = array[i], tmp2;
				for (j = i; j > left && (tmp2 = array[j - 1]) > tmp; --j)
					array[j] = tmp2;
				array[j] = tmp;
			}
			return;
		}
		int l = left;
		while (l < right && (array[l] & digit) == 0)
			++l;
		for (int r = l + 1; r < right; ++r) {
			long i = array[r];
			if ((i & digit) == 0) {
				array[r] = array[l];
				array[l++ ] = i;
			}
		}
		if ((digit = Long.highestOneBit(use & digit - 1)) == 0) return;
		sort(array, left, l, use, digit);
		sort(array, l, right, use, digit);
	}
}

class IntMath {

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

	public static int gcd(int... array) {
		int ret = array[0];
		for (int i = 1; i < array.length; ++i)
			ret = gcd(ret, array[i]);
		return ret;
	}

	public static long gcd(long a, long b) {
		while (a != 0)
			if ((b %= a) != 0) a %= b;
			else return a;
		return b;
	}

	public static long gcd(long... array) {
		long ret = array[0];
		for (int i = 1; i < array.length; ++i)
			ret = gcd(ret, array[i]);
		return ret;
	}

	public static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	public static int pow(int a, int b) {
		int ans = 1;
		for (int mul = a; b > 0; b >>= 1, mul *= mul)
			if ((b & 1) != 0) ans *= mul;
		return ans;
	}

	public static long pow(long a, long b) {
		long ans = 1;
		for (long mul = a; b > 0; b >>= 1, mul *= mul)
			if ((b & 1) != 0) ans *= mul;
		return ans;
	}

	public static int pow(int a, long b, int mod) {
		if (b < 0) b = b % (mod - 1) + mod - 1;
		long ans = 1;
		for (long mul = a; b > 0; b >>= 1, mul = mul * mul % mod)
			if ((b & 1) != 0) ans = ans * mul % mod;
		return (int)ans;
	}

	public static int pow(long a, long b, int mod) {
		return pow((int)(a % mod), b, mod);
	}

	public static int floorsqrt(long n) {
		return (int)Math.sqrt(n + 0.1);
	}

	public static int ceilsqrt(long n) {
		return n <= 1 ? (int)n : (int)Math.sqrt(n - 0.1) + 1;
	}
}