Vivek initially has an empty array a and some integer constant m.

He performs the following algorithm:

  1. Select a random integer x uniformly in range from 1 to m and append it to the end of a. 
  2. Compute the greatest common divisor of integers in a. 
  3. In case it equals to 1, break 
  4. Otherwise, return to step 1. 



Find the expected length of a. It can be shown that it can be represented as P/Q where P and Q are coprime integers and Q≠ 0 \pmod{10^9+7}. Print the value of P ⋅ Q^{-1} \pmod{10^9+7}.

Input

The first and only line contains a single integer m (1 ≤ m ≤ 100000).

Output

Print a single integer — the expected length of the array a written as P ⋅ Q^{-1} \pmod{10^9+7}.

Examples

Input


1


Output


1


Input


2


Output


2


Input


4


Output


333333338

Note

In the first example, since Vivek can choose only integers from 1 to 1, he will have a=[1] after the first append operation, and after that quit the algorithm. Hence the length of a is always 1, so its expected value is 1 as well.

In the second example, Vivek each time will append either 1 or 2, so after finishing the algorithm he will end up having some number of 2's (possibly zero), and a single 1 in the end. The expected length of the list is 1⋅ 1/2 + 2⋅ (1)/(2^2) + 3⋅ (1)/(2^3) + … = 2.
//package round548;
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 D3 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int mod = 1000000007;
		int n = ni();
		int[] invs = enumInvs(n, mod);
		int[] lpf = enumLowestPrimeFactors(n);
		int[] mobs = enumMobiusByLPF(n, lpf);
		
		// 4/3+2 = 10/3
		// 2 = 2
		
		long ans = 0;
		long ans2 = 0;
		for(int d = 2;d <= n;d++) {
			// sum (t/n)^k = 1/(1-t/n) = n/(n-t)
			ans -= mobs[d] * (long)invs[n-n/d];
			ans2 += mobs[d];
		}
		ans = ans*n + ans2 + 1;
		ans %= mod;
		if(ans < 0)ans += mod;
		out.println(ans);
	}
	
	public static int[] enumMobiusByLPF(int n, int[] lpf)
	{
		int[] mob = new int[n+1];
		mob[1] = 1;
		for(int i = 2;i <= n;i++){
			int j = i/lpf[i];
			if(lpf[j] == lpf[i]){
//				mob[i] = 0;
			}else{
				mob[i] = -mob[j];
			}
		}
		return mob;
	}

	
	public static int[] enumInvs(int n, int mod)
	{
		int[] inv = new int[n+1];
		inv[1] = 1;
		for(int i = 2;i <= n;i++){
			inv[i] = (int)(inv[mod%i]*(long)(mod-mod/i)%mod);
		}
		return inv;
	}

	
	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 int[] enumDivisorsFast(int n, int[] lpf)
	{
		int[] divs = {1};
		while(lpf[n] > 0){
			int p = lpf[n];
			int e = 0;
			for(;p == lpf[n];e++, n /= p);
			int olen = divs.length;
			divs = Arrays.copyOf(divs, olen*(e+1));
			for(int i = olen;i < divs.length;i++)divs[i] = divs[i-olen] * p;
		}
		return divs;
	}

	
	public static int[] enumLowestPrimeFactors(int n) {
		int tot = 0;
		int[] lpf = new int[n + 1];
		int u = n + 32;
		double lu = Math.log(u);
		int[] primes = new int[(int) (u / lu + u / lu / lu * 1.5)];
		for (int i = 2; i <= n; i++)
			lpf[i] = i;
		for (int p = 2; p <= n; p++) {
			if (lpf[p] == p)
				primes[tot++] = p;
			int tmp;
			for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) {
				lpf[tmp] = primes[i];
			}
		}
		return lpf;
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D3().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private 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 boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private 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 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 int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private 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 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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
