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.Scanner;
import java.io.PrintWriter;

public class B {
    
    int N;
    
    int start;
    
    int[] data;
    
    private B read() {
        Scanner sc = new Scanner( System.in );
        N = sc.nextInt();
        return this;
    }
    
    private B init() {
        data = new int[2*N];
        for (int i=0; i<N; i++) {
            data[i] = i+1;
        }
        start = 0;
        return this;
    }
    
    private void step(int k) {
        int prev = 0;
        for ( int now=start; now<start+N; now+=k ) {
            int next = data[now];
            data[now] = prev;
            prev = next;
        }
        data[start+N] = prev;
        start++;
    }
    
    private B solve() {
        for (int i=2; i<N+1; i++) {
            step( i );
        }
        return this;
    }
    
    private B save() {
        PrintWriter pw = new PrintWriter( System.out );
        for (int i=start; i<start+N; i++) {
            if (i > start) {
                pw.print( " " );
            }
            pw.print( data[i] );
        }
        pw.close();
        return this;
    }
            
    public static void main(String[] args) {
        new B().read().init().solve().save();
    }
    
}