John Doe has found the beautiful permutation formula.

Let's take permutation p = p1, p2, ..., pn. Let's define transformation f of this permutation: 

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where k (k > 1) is an integer, the transformation parameter, r is such maximum integer that rk ≤ n. If rk = n, then elements prk + 1, prk + 2 and so on are omitted. In other words, the described transformation of permutation p cyclically shifts to the left each consecutive block of length k and the last block with the length equal to the remainder after dividing n by k. 

John Doe thinks that permutation f(f( ... f(p = [1, 2, ..., n], 2) ... , n - 1), n) is beautiful. Unfortunately, he cannot quickly find the beautiful permutation he's interested in. That's why he asked you to help him.

Your task is to find a beautiful permutation for the given n. For clarifications, see the notes to the third sample.

Input

A single line contains integer n (2 ≤ n ≤ 106).

Output

Print n distinct space-separated integers from 1 to n — a beautiful permutation of size n.

Examples

Input

2


Output

2 1 


Input

3


Output

1 3 2 


Input

4


Output

4 2 3 1 

Note

A note to the third test sample: 

  * f([1, 2, 3, 4], 2) = [2, 1, 4, 3]
  * f([2, 1, 4, 3], 3) = [1, 4, 2, 3]
  * f([1, 4, 2, 3], 4) = [4, 2, 3, 1]
import java.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

// Shifting
// 2013/03/23
public class P286B{
	Scanner sc=new Scanner(System.in);

	int n;

	void run(){
		n=sc.nextInt();
		solve();
	}

	void solve(){
		int[] a=new int[2*n];
		for(int i=0; i<n; i++){
			a[i]=i+1;
		}
		int os=0;
		for(int d=2; d<=n; d++){
			for(int i=(n-1)/d*d; i+os>=0; i-=d){
				a[min(i+(d-1), n-1)+(os+1)]=a[i+os];
			}
			a[os]=0;
			os++;
		}
		StringBuilder sb=new StringBuilder();
		for(int i : a){
			if(i>0){
				sb.append(i).append(' ');
			}
		}
		println(sb.toString().trim());
	}

	void println(String s){
		System.out.println(s);
	}

	public static void main(String[] args){
		Locale.setDefault(Locale.US);
		new P286B().run();
	}
}
