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.io.*;
import java.util.*;

public class Contest176 {

    public static void main(String[] args) throws IOException {
        new Contest176().run();
    }

    public void solve() throws IOException {
        int n = nextInt();
        int p[] = new int[2 * n + 1];
        for(int i = 1; i <= n; ++i)
            p[i] = i;

        int first = 1;
        int last = n;
        for(int len = 2; len <= n; ++len, ++first, ++last) {
            int cur = last - n % len + 1;
            while(cur >= first) {
                p[Math.min(last + 1, cur + len)] = p[cur];
                cur -= len;
            }
        }

        for(int i = first; i <= last; ++i)
            out.print(p[i] + " ");
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    String nextToken() throws IOException {
        while( in == null || !in.hasMoreTokens() ) {
            in = new StringTokenizer(br.readLine());
        }

        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    void run() throws IOException {
        boolean oj = System.getProperty( "ONLINE_JUDGE" ) != null;
        Reader reader = new InputStreamReader( oj ? System.in : new FileInputStream("input.txt"));
        Writer writer = new OutputStreamWriter( oj ? System.out : new FileOutputStream("output.txt"));
        br = new BufferedReader(reader);
        out = new PrintWriter(writer);

        solve();

        out.close();
    }
}