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.BufferedReader;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.InputStreamReader;
	import java.io.PrintWriter;
	import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
	import java.util.HashMap;
	import java.util.InputMismatchException;
	import java.util.Iterator;
	import java.util.List;
	import java.util.Random;
	import java.util.TreeMap;
	import java.util.TreeSet;
	                 
	                 
	                 
	                 
	                 
	                public class Solution2 implements Runnable
	                {
	                    static final long MAX = 464897L;
	                    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);
	                        }
	                    }
	                     
	                    public static void main(String args[]) throws Exception
	                    {
	                        new Thread(null, new Solution2(),"Solution2",1<<26).start();
	                    }   
	                    static long gcd(long a, long b) 
	                    { 
	                      if (b == 0) 
	                        return a; 
	                      return gcd(b, a % b);  
	                    } 
	                    static long lcm(long a,long b) {
	                        return (a*b)/gcd(a,b);
	                    }
	                    int maxn = 1000005;
	                    long MOD = 998244353;
	                    long prime = 29;
	                    ArrayList<Integer> adj[];
	                    TreeMap<Integer,ArrayList<Integer>> tmap = new TreeMap();
	                   
	                    public void run() 
	                    {
	                        InputReader sc = new InputReader(System.in);
	                        PrintWriter w = new PrintWriter(System.out);
	                        long ans = 0;
	                        int n = sc.nextInt();
	                        if(n == 1) {
	                        	w.println("1");
	                        	w.close();
	                        	System.exit(0);
	                        }	
	                        if(n == 2) {
	                        	w.println(2);
	                        	w.close();
	                        	System.exit(0);
	                        }
	                        ans = 2;
	                        long rem = 0;
	                        for(int i = 3;i <= n;i++) {
	                        	ans = (ans * i) % MOD;
	                        	rem = ((rem + (i - 2)) % MOD * i) % MOD;
	                        	ans = (ans + rem) % MOD;
	                        }
	                        w.println(ans);
	                        w.close();
	                    }
	                    StringBuilder build = new StringBuilder();
	                    int ptr = 0;
	                    int[] ar = new int[5*5*4*3*2*1];
	                    void sort(int[] arr) {
	                    	int n = arr.length;
	                    	boolean f = false;
	                    	while(!f) {
	                    		for(int i = 0;i < n;i++) {
	                    			ar[ptr++] = arr[i];
	                    		}
	                    		int i;
	                    		for( i = n-2;i >= 0;i--) {
	                    			if(arr[i] < arr[i+1]) {
	                    				break;
	                    			}
	                    		}
	                    		if(i == -1) {
	                    			f = true;
	                    		}else {
	                    			int ceilIndex = findCeil(arr, arr[i], i+1, n-1);
	                    			int temp = arr[i];
	                    			arr[i] = arr[ceilIndex];
	                    			arr[ceilIndex] = temp;
	                    			reverse(arr, i+1, n-1);
	                    		}
	                    	}
	                    }
	                    void reverse(int arr[], int l, int h) 
	                    { 
	                       while (l < h) 
	                       { 
	                           int temp = arr[l];
	                           arr[l] = arr[h];
	                           arr[h] = temp;
	                           l++; 
	                           h--; 
	                       } 
	                    } 
	                    long[] fact = new long[1000005];
                        void pre() {
                            fact[0] = 1;
                            for(int i = 1;i < fact.length;i++) {
                                fact[i] = (fact[i-1] * i) % MOD;
                            }
                        }
	                    int findCeil (int str[],  int first, int l, int h) 
	                    { 
	                        // initialize index of ceiling element 
	                        int ceilIndex = l; 
	                      
	                        // Now iterate through rest of the elements and find 
	                        // the smallest character greater than 'first' 
	                        for (int i = l+1; i <= h; i++) 
	                          if (str[i] > first && str[i] < str[ceilIndex]) 
	                                ceilIndex = i; 
	                      
	                        return ceilIndex; 
	                    } 
	                    long calc(long a,long num) {
	                    	long oc = num/a - 1;
	                    	long ans = (oc * (oc + 1)/2) * a + oc;
	                    	return ans;
	                    }
	                    int[][] generator(int seed,int n,int m) {
	                    	Random generator = new Random(seed);
	                    	int[][] matrix = new int[n][m];
	                    	for(int i = 0;i < n;i++) {
	                    		for(int j = 0;j < m;j++) {
	                    			matrix[i][j] = generator.nextInt(2);
	                    		}
	                    	}
	                    	return matrix;
	                    }
	                    int rec(int[][] matrix,int n,int m) {
	                    	int ans = 1;
	                    	for(int i = 0;i < n;i++) {
	                    		for(int j = 0;j < m;j++) {
	                    			if(matrix[i][j] != 1) {
	                    				boolean res = false;
	                    				if(i - 1 >= 0) {
	                    					res = res | (matrix[i-1][j] != 1);
	                    				}
	                    				if(i + 1 < n) {
	                    					res = res | (matrix[i+1][j] != 1);
	                    				}
	                    				if(j - 1 >= 0) {
	                    					res = res | (matrix[i][j-1] != 1);
	                    				}
	                    				if(j + 1 < m) {
	                    					res = res | (matrix[i][j+1] != 1);
	                    				}
	                    				if(res) {
	                    					matrix[i][j] = 1;
	                    					int pos = i * m + (j);
	                    					
	                    				    int grundy = rec(matrix,n,m);
	                    					ans = ans & grundy;
	                    					
	                    					matrix[i][j] = 0;
	                    				}
	                    			}
	                    		}
	                    	}
	                    	ans = ans ^ 1;
	                    	return ans;
	                    }
	                    ArrayList<Integer> list[];
	                    HashMap<List<Integer>,Integer> M = new HashMap();
	                    int ID = 1;
	                    void dfs(int v,int[] my,int prev) {
	                    	list[v] = new ArrayList();
	                    	for(int i = 0;i < adj[v].size();i++) {
	                    		int u = adj[v].get(i);
	                    		if(u == prev) {
	                    			continue;
	                    		}
	                    		dfs(u,my,v);
	                    		list[v].add(my[u]);
	                    	}
	                    	Collections.sort(list[v]);
	                    	if(M.containsKey(list[v])) {
	                    		my[v] = M.get(list[v]);
	                    	}
	                    	else {
	                    		my[v] = ID;
	                    		M.put(list[v], ID);
	                    		ID++;
	                    	}
	                    }
	                    static boolean isPrime(long n) 
	                    { 
	                        // Corner cases 
	                        if (n <= 1) return false; 
	                        if (n <= 3) return true; 
	                      
	                        // This is checked so that we can skip  
	                        // middle five numbers in below loop 
	                        if (n % 2 == 0 || n % 3 == 0) return false; 
	                      
	                        for (int i = 5; i * i <= n; i = i + 6) 
	                            if (n % i == 0 || n % (i + 2) == 0) 
	                            return false; 
	                      
	                        return true; 
	                    } 
	                    static class SegTreeLazy{
	                		long[] segTree;
	                		long[] lazy;
	                		public SegTreeLazy(int n){
	                			segTree = new long[4*n];
	                			lazy = new long[4*n];
	                		}
	                		void build(int l,int r,int pos,long[] arr) {
	                			if(l == r) {
	                				segTree[pos] = arr[l];
	                				return;
	                			}
	                			int mid = (l + r)/2;
	                			build(l, mid, 2*pos+1, arr);
	                			build(mid+1, r, 2*pos+2, arr);
	                			segTree[pos] = segTree[2*pos+1] + segTree[2*pos+2];
	                		}
	                		void update(int l,int r,int pos,int ind,long val) {
	                			if(l > ind || r < ind) {
	                				return;
	                			}
	                			if(l == r) {
	                				segTree[pos] = val;
	                				return;
	                			}
	                			int mid = (l + r)/2;
	                			update(l, mid, 2*pos+1, ind, val);
	                			update(mid+1, r, 2*pos+2, ind, val);
	                			segTree[pos] = segTree[2*pos+1] + segTree[2*pos+2];
	                		}
	                		long query(int l,int r,int start,int end,int pos) {
	                			if(l > r || l > end || r < start) {
	                				return 0;
	                			}
	                			if(l >= start && r <= end) {
	                				return segTree[pos];
	                			}
	                			int mid = (l + r)/2;
	                			long p1 = query(l, mid, start, end, 2*pos+1);
	                			long p2 = query(mid+1, r, start, end, 2*pos+2);
	                			return p1 + p2;
	                		}
	                	}
	                    int count = 0;
	                   
	                    boolean[] visited;
	                    int[] parent;
	                    void dfs(int a) {
	                    	boolean leaf=  false;
	                    	visited[a] = true;
	                    	Iterator<Integer> it = adj[a].iterator();
	                    	while(it.hasNext()) {
	                    		int x = it.next();
	                    		if(!visited[x]) {
	                    			parent[x] = a;
	                    			leaf = true;
	                    			dfs(x);
	                    		}
	                    	}
	                    	if(!leaf) {
	                    		count++;
	                    	}
	                    }
	                   
	                    class Pair implements Comparable<Pair>{
	                        long a;
	                        long b;
	                        long c;
	                        Pair(long a,long b,long c){
	                            this.b = b;
	                            this.a = a;
	                            this.c = c;
	                        }
	                        public boolean equals(Object o) {
	                            Pair p = (Pair)o;
	                            return this.a == p.a && this.b == this.b;
	                        }
	                        public int hashCode(){
	                            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
	                        }
	                        public int compareTo(Pair p) {
	                            return Long.compare(this.a,p.a);
	                        }
	                    }
	                    
	                }