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.*;
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();
    }
}