There are N squares lining up in a row, numbered 1 through N from left to right. Initially, all squares are white. We also have N-1 painting machines, numbered 1 through N-1. When operated, Machine i paints Square i and i+1 black.

Snuke will operate these machines one by one. The order in which he operates them is represented by a permutation of (1, 2, ..., N-1), P, which means that the i-th operated machine is Machine P_i.

Here, the score of a permutation P is defined as the number of machines that are operated before all the squares are painted black for the first time, when the machines are operated in the order specified by P. Snuke has not decided what permutation P to use, but he is interested in the scores of possible permutations. Find the sum of the scores over all possible permutations for him. Since this can be extremely large, compute the sum modulo 10^9+7.

Constraints

* 2 \leq N \leq 10^6

Input

Input is given from Standard Input in the following format:


N


Output

Print the sum of the scores over all possible permutations, modulo 10^9+7.

Examples

Input

4


Output

16


Input

2


Output

1


Input

5


Output

84


Input

100000


Output

341429644
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	static void solve()
	{
		int n = ni();
		int mod = 1000000007;
		long[][] res =  guessLeaned(1000000007, 
				1, 4, 16, 84, 516, 3696, 30096, 275040, 2786400, 31000320, 375736320, 928152292
				);
		
		long[] u = {1, 4, 16};
		for(int i = 3;i <= n;i++){
			long v = f(res, u, i, mod);
			for(int j = 0;j < 2;j++){
				u[j] = u[j+1];
			}
			u[2] = v;
		}
		out.println(u[0]);
	}
	
	public static long f(long[][] ged, long[] prevs, long x, int mod)
	{
		int n = ged.length;
		assert prevs.length == n-1;
		x -= n-1;
		
		long s = 0;
		long tar = 0;
		for(int i = 0;i < n;i++){
			long co = 0;
			for(int j = ged[i].length-1;j >= 0;j--){
				co = (co * x + ged[i][j]) % mod;
			}
			if(i < n-1){
				s += co * prevs[i];
				s %= mod;
			}else{
				tar = co;
			}
		}
		
		long ret = -invl(tar, mod) * s % mod;
		if(ret < 0)ret += mod;
		return ret;
	}
	
	public static long[][] guessLeaned(int mod, long... a)
	{
		int n = a.length;
		
		// #formula >= #variable
		// n-r+2 >= r(r+1)/2
		for(int r = n;r >= 1;r--){
			if(n-r+2 < r*(r+1)/2)continue;
			int[][] M = new int[n-r+2][r*(r+1)/2];
			for(int i = 0;i < n-r+1;i++){
				int p = 0;
				for(int j = 0;j < r;j++){
					long prod = 1;
					for(int k = 0;k <= r-j-1;k++){
						M[i][p++] = (int)(prod*a[i+j]%mod);
						prod = prod * i % mod;
					}
				}
			}
			M[n-r+1][0] = 1;
			
			int[] v = new int[n-r+2];
			v[n-r+1] = 1;
			
			Result res = gaussElimination(M, v, mod);
			if(res.exists){
				long[][] ret = new long[r][];
				int p = 0;
				for(int i = 0;i < r;i++){
					ret[i] = new long[r-i];
					for(int j = 0;j < r-i;j++){
						ret[i][j] = res.sol[p++];
					}
				}
				return ret;
			}
		}
		return null;
	}
	
	public static Result gaussElimination(int[][] M, int[] v, int mod)
	{
		int n = M.length, m = M[0].length;
		int[] head = new int[n];
		
		// if not needed, comment out.
		for(int[] row : M){
			for(int i = 0;i < row.length;i++){
				row[i] %= mod;
				if(row[i] < 0)row[i] += mod;
			}
		}
		
		// Forward Elimination
		int row = 0;
		for(int col = 0;col < m;col++){
			// select pivot
			boolean pivotFound = false;
			out:
			for(int prow = row;prow < n;prow++){
				if(M[prow][col] != 0){
					// pivot found
					if(prow != row){
						// swap rows
						for(int k = 0;k < m;k++){
							int u = M[prow][k]; M[prow][k] = M[row][k]; M[row][k] = u;
						}
						int dum = v[prow]; v[prow] = v[row]; v[row] = dum;
					}
					pivotFound = true;
					break out;
				}
			}
			if(!pivotFound)continue;
			head[row] = col;
			
			// diag to 1
			long imul = invl(M[row][col], mod);
			for(int k = 0;k < m;k++){
				M[row][k] = (int)(M[row][k] * imul % mod);
			}
			v[row] = (int)(v[row] * imul % mod);
			
			for(int j = row+1;j < n;j++){
				if(M[j][col] != 0){
					long mul = mod-M[j][col];
					for(int k = col;k < m;k++){
						M[j][k] = (int)((M[j][k] + M[row][k] * mul) % mod);
					}
					v[j] = (int)((v[j] + v[row] * mul) % mod);
				}
			}
			row++;
		}
		
		Result ret = new Result();
		ret.mat = M;
		for(int i = row;i < n;i++){
			if(v[i] != 0){
				ret.rank = row;
				ret.exists = false;
				return ret;
			}
		}
		
		for(int i = row-1;i >= 0;i--){
			for(int j = i-1;j >= 0;j--){
				if(M[j][head[i]] != 0){
					long mul = mod-M[j][head[i]];
					for(int k = head[i];k < m;k++){
						M[j][k] = (int)((M[j][k] + M[i][k] * mul) % mod);
					}
					v[j] = (int)((v[j] + v[i] * mul) % mod);
				}
			}
		}
		
		int[] retv = new int[m];
		for(int i = 0;i < row;i++){
			retv[head[i]] = v[i];
		}
		
		ret.sol = retv;
		ret.rank = row;
		ret.exists = true;
		return ret;
	}
	
	public static class Result
	{
		public int[][] mat;
		public int[] sol;
		public int rank;
		public boolean exists;
	}
	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}


	
	public static long C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n)
			return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}

	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}
