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.io.*;
import static java.lang.Math.*;

public class cf2 implements Runnable {   
	
	final static long mod =  998244353;
	
	static long modExp(long x, long y) {
		
		if(y == 0)
			return 1;
		
		if(y == 1)
			return x;
		
		long ret = modExp(x, y / 2);
		ret = ret * ret % mod;
		
		if(y % 2 == 1)
			ret = ret * x % mod;
		
		return ret;
	}
	
	public void run() {
			
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		int n = s.nextInt();
		
		long[] fact = new long[n + 1]; fact[0] = 1;
		
		for(int i = 1; i <= n; i++)
			fact[i] = fact[i - 1] * i % mod;
		
		long[] invFact = new long[n + 1]; invFact[0] = 1;
		
		for(int i = 1; i <= n; i++)
			invFact[i] =  modExp(fact[i], mod - 2);
		
		long res = fact[n];
		
		for(int i = 2; i <= n - 1; i++) 
			res = (res + (fact[n] - fact[n] * invFact[i] % mod + mod) % mod) % mod;
		
		w.println(res);
		
		w.close();
	}
	
	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 String nextLine() {
			
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			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);
		}
	
	}

	public static void main(String args[]) throws Exception {
		new Thread(null, new cf2(),"cf2",1<<26).start();
	}
}   