Let n be an integer. Consider all permutations on integers 1 to n in lexicographic order, and concatenate them into one big sequence p. For example, if n = 3, then p = [1, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2, 3, 2, 1]. The length of this sequence will be n ⋅ n!.

Let 1 ≤ i ≤ j ≤ n ⋅ n! be a pair of indices. We call the sequence (p_i, p_{i+1}, ..., p_{j-1}, p_j) a subarray of p. Its length is defined as the number of its elements, i.e., j - i + 1. Its sum is the sum of all its elements, i.e., ∑_{k=i}^j p_k. 

You are given n. Find the number of subarrays of p of length n having sum (n(n+1))/(2). Since this number may be large, output it modulo 998244353 (a prime number). 

Input

The only line contains one integer n (1 ≤ n ≤ 10^6), as described in the problem statement.

Output

Output a single integer — the number of subarrays of length n having sum (n(n+1))/(2), modulo 998244353.

Examples

Input


3


Output


9


Input


4


Output


56


Input


10


Output


30052700

Note

In the first sample, there are 16 subarrays of length 3. In order of appearance, they are:

[1, 2, 3], [2, 3, 1], [3, 1, 3], [1, 3, 2], [3, 2, 2], [2, 2, 1], [2, 1, 3], [1, 3, 2], [3, 2, 3], [2, 3, 1], [3, 1, 3], [1, 3, 1], [3, 1, 2], [1, 2, 3], [2, 3, 2], [3, 2, 1]. 

Their sums are 6, 6, 7, 6, 7, 5, 6, 6, 8, 6, 7, 5, 6, 6, 7, 6. As (n(n+1))/(2) = 6, the answer is 9.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int MOD = 998244353;
            NumberTheory.MODULO = MOD;
            long[] f = NumberTheory.factorials(n);
            long[] inv = NumberTheory.inverseFactorials(n);

            int res = 0;
            for (int i = 1; i < n; ++i) {
                res = NumberTheory.add(res, NumberTheory.multiply(NumberTheory.multiply((int) f[n], (int) inv[n - i + 1]), NumberTheory.subtract((int) f[n - i + 1], 1)));
//            res += multiply(multiply((int) f[n], (int) inv[n - i + 1]), n - i - 1);
            }

            out.println(NumberTheory.add(res, 1));
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(readLine());
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }

    }

    static class NumberTheory {
        public static int MODULO = 1_000_000_007;

        public static int multiply(int a, int b) {
            long product = a * (long) b;
            if (product >= MODULO)
                product %= MODULO;
            return (int) product;
        }

        public static int multiply(int a, int b, int mod) {
            long product = a * (long) b;
            if (product >= mod)
                product %= mod;
            return (int) product;
        }

        public static int add(int a, int b) {
            long sum = a + (long) b;
            if (sum >= MODULO)
                sum -= MODULO;
            return (int) sum;
        }

        public static int subtract(int a, int b) {
            return subtract(a, b, MODULO);
        }

        public static int subtract(int a, int b, int modulo) {
            if (a >= b)
                return a - b;
            else
                return a - b + modulo;
        }

        public static long[] factorials(final int nInclusive) {
            return factorials(nInclusive, MODULO);
        }

        public static long[] factorials(final int nInclusive, int mod) {
            long[] fac = new long[nInclusive + 1];
            fac[0] = fac[1] = 1L;
            for (int i = 2; i <= nInclusive; i++) {
                fac[i] = fac[i - 1] * i;
                if (fac[i] >= mod)
                    fac[i] %= mod;
            }
            return fac;
        }

        public static long[] inverseFactorials(final int nInclusive) {
            return inverseFactorials(nInclusive, MODULO);
        }

        public static long[] inverseFactorials(final int nInclusive, int modulo) {
            long[] f = factorials(nInclusive, modulo);
            f[nInclusive] = inverse((int) f[nInclusive], modulo);

            for (int i = nInclusive - 1; i >= 2; --i)
                f[i] = multiply((int) f[i + 1], i + 1, modulo);

            return f;
        }

        public static int powmod(int a, long n, int mod) {
            long res = 1L;
            long half = a;
            while (n != 0) {
                if ((n & 1) == 1)
                    res = res * half % mod;
                half = half * half % mod;
                n >>= 1;
            }
            return (int) res;
        }

        public static int inverse(int a, int modulo) {
            return inverse(a, modulo, true);
        }

        public static int inverse(int a, int b, boolean usePow) {
            if (usePow) {
                return powmod(a, b - 2, b);
            } else {
                int[] coef = new int[3];
                extendedEuclideanAlgo(a, b, coef);
                if (coef[0] != 1)
                    throw new RuntimeException("gcd must be 1 to have modular inverse");
                else {
                    int result = (coef[1] % b + b) % b;
                    return result;
                }
            }
        }

        public static void extendedEuclideanAlgo(int a, int b, int[] res) {
            if (b == 0) {
                res[0] = a;
                res[1] = 1;
                res[2] = 0;
                return;
            }
            extendedEuclideanAlgo(b, a % b, res);
            int temp = res[2];
            res[2] = res[1] - a / b * res[2];
            res[1] = temp;
        }

    }
}

