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.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
import java.io.*;
import java.math.*;




public class Solution
{
	
	static StringBuilder sb;
	static dsu dsu;
	static long fact[];
	static int mod=(int)(998244353 );
	
	
	
	static void solve()
    {
		int n=i();
		 fact=new long[(int)1e6+10];
         fact[0]=fact[1]=1;
         
         for(int i=2;i<fact.length;i++)
         {
        	fact[i]=((long)(i%mod)*1L*(long)(fact[i-1]%mod))%mod; 
         }
         long ans=0;
        //dn=(d(n-1)+(n-1)!-1)*n
         //for(int i=1;i<=n;i++) 
         //{
        	 
        	long dp[]=new long[1000000+10];
        	dp[1]=1;
        	dp[2]=2;
        	for(int i=3;i<=n;i++)
        	{
        		dp[i]=(i*(dp[i-1]+(fact[i-1]-1)%mod+mod)%mod)%mod;
        	}
        	
        	 
        	 
        	 
         System.out.println(dp[n]);
		
		
    }
	
    public static void main(String[] args)
	 {
		 sb=new StringBuilder();
	     int test=1;
	    for(int tt=1;tt<=test;tt++) 
	    {
	         solve();
	    }
	     System.out.println(sb);
	 }
	 
//*******************************************NCR%P*******************************************************	 
	 static long ncr(int n, int r)
	 {
		 if(r>n)
			 return (long)0;
		 
		 long res=fact[n]%mod;
		 //System.out.println(res);
		 res=((long)(res%mod)*(long)(p(fact[r],mod-2)%mod))%mod;
		 res=((long)(res%mod)*(long)(p(fact[n-r],mod-2)%mod))%mod;
		 //System.out.println(res);
		 return res;
		
		 
	 }
		static long p(long x, long y)//POWER FXN //
		{
			if(y==0)
				return 1;
			
			long res=1;
			while(y>0)
			{
				if(y%2==1)
				{
					res=(res*x)%mod;
					y--;
				}
				
				x=(x*x)%mod;
				y=y/2;
				
				
			}
			return res;
		}
		

//*******************************************END*******************************************************
	 
	 
	 
	 
	 
	 //*********************************Disjoint set union*************************//
	 static class dsu
	 {
		 int parent[];
		 dsu(int n)
		 {
			 parent=new int[n];
			 for(int i=0;i<n;i++)
				 parent[i]=-1;
		 }
		 int find(int a)
		 {
			 if(parent[a]<0)
				 return a;
			 else
			 {
				 int x=find(parent[a]);
				 parent[a]=x;
				 return x;
			 }
		 }
		 void merge(int a,int b)
		 {
			 a=find(a);
			 b=find(b);
			 if(a==b)
				 return;
			 parent[b]=a;
		 }
	 }
	 
	 
	 
//*******************************************PRIME FACTORIZE *****************************************************************************************************//
	 static TreeMap<Integer,Integer> prime(long n)
	 {
		 TreeMap<Integer,Integer>h=new TreeMap<>();
		 long num=n;
		 for(int i=2;i<=Math.sqrt(num);i++)
		 {
			 if(n%i==0)
			 {
				 int nt=0;
				 while(n%i==0) {
					 n=n/i;
					 nt++;
				 }
				 h.put(i, nt);
			 }
		 }
		 if(n!=1)
			 h.put((int)n, 1);
		 return h;
		 
	 }
	 
	
	
//*************CLASS PAIR ***********************************************************************************************************************************************
	    static class pair implements Comparable<pair>
	    {
	        int x;
	        long  y;

	        pair(int x, long y) {
	            this.x = x;
	            this.y = y;
	        }
	        public int compareTo(pair o)
	        {
	        	return(int) (y-o.y);
	        	
	        }
			
	       
	    }
//*************CLASS PAIR *****************************************************************************************************************************************************
	
	
	

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

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

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

        public int Int() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String String() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return String();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

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

        public void flush() {
            writer.flush();
        }
    }

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);
   

    public static int[] sort(int[] a) {
        int n = a.length;
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
        return a;
    }

    public static long pow(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                res = (res * x);// % modulus;
                y--;

            }
            x = (x * x);// % modulus;
            y = y / 2;
        }
        return res;
    }
//GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }
    //****************LOWEST COMMON MULTIPLE   *************************************************************************************************************************************

    public static long lcm(long x, long y) {
        return (x * (y / gcd(x, y)));
    }
//INPUT PATTERN******************************************************************************************************************************************************************
    public static int i() {
        return in.Int();
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static String s() {
        return in.String();
    }

    public static int[] readArray(int n) {
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = i();
        }
        return A;
    }

    public static long[] readArray(long n) {
        long A[] = new long[(int) n];
        for (int i = 0; i < n; i++) {
            A[i] = l();
        }
        return A;
    }

}






	