Problem: 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 is 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. 

You are given n. Find the number of distinct subarrays of P. 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 distinct subarrays, modulo 998244353.

Examples

Input


2


Output


8


Input


10


Output


19210869

Note

In the first example, the sequence P = [1, 2, 2, 1]. It has eight distinct subarrays: [1], [2], [1, 2], [2, 1], [2, 2], [1, 2, 2], [2, 2, 1] and [1, 2, 2, 1]. 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;
 
public class fast implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            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 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 readString();
        }
        
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
	
	class pair implements Comparable<pair>{
		int x;
		int y;
		pair(int xi, int yi){
			x=xi;
			y=yi;
		}
		@Override
		public int compareTo(pair other){
			if(this.x>other.x)
				return 1;
			if(this.x<other.x)
				return -1;
			return 0;
		}	
	} 
	
    public static void main(String args[]) throws Exception {
        new Thread(null, new fast(),"fast",1<<26).start();
    }
	
	public void sortbyColumn(int arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<int[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final int[] entry1,  
                             final int[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            else if(entry1[col] < entry2[col])
                return -1;
			return 0;
          } 
        });  // End of function call sort(). 
    }
	
	public void sortbyColumn(long arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<long[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final long[] entry1,  
                             final long[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            else if(entry1[col] < entry2[col])
                return -1;
			return 0;
          } 
        });  // End of function call sort(). 
    }
	
	long power(long x, long y, long p){  
        long res = 1;      
        x = x % p;  
        while (y > 0) 
        { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }

	long ncr(int n, int r, long p){  
        long C[]=new long[r+1]; 
        C[0] = 1; 
        for (int i = 1; i <= n; i++) 
        { 
            for (int j = Math.min(i, r); j > 0; j--) 
                C[j] = (C[j] + C[j-1])%p; 
        } 
        return C[r]; 
    }
	
    public void run(){
        Scanner s = new Scanner(System.in);
        PrintWriter w = new PrintWriter(System.out);
		
		int n=s.nextInt();
		long fact[]=new long[n+1],dp[]=new long[n+1],mod=998244353L;
		fact[0]=1;
		for(int i=1;i<=n;i++){
			fact[i]=(fact[i-1]*i)%mod;
		}
		dp[1]=1;
		for(int i=2;i<=n;i++){
			dp[i]=(fact[i]+(dp[i-1]-1)*i)%mod;
		}
		w.println(dp[n]);
		
		w.close();
    }
}