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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/*
 public class _287D {

 }

 */
public class _287D {
  public void solve() throws FileNotFoundException {
    InputStream inputStream = System.in;

    InputHelper in = new InputHelper(inputStream);

    // actual solution
    int n = in.readInteger();

    int[] a = new int[2 * n];

    for (int i = 0; i < n; i++) {
      a[i] = i + 1;
    }

    int s = 0, e = n - 1;

    for (int i = 2; i <= n; i++) {

      int t1 = a[s];
      int t2 = -1;
      for (int j = s + i;; j += i) {
        if (j > e + 1) {
          j = e + 1;
        }
        t2 = a[j];
        a[j] = t1;
        t1 = t2;

        if (j == e + 1)
          break;
      }

      s++;
      e++;
    }

    StringBuilder sb = new StringBuilder();

    for (int i = n - 1; i < 2 * n - 1; i++) {
      sb.append(a[i] + " ");
    }

    System.out.println(sb.toString());
    // end here
  }

  public static void main(String[] args) throws FileNotFoundException {
    (new _287D()).solve();
  }

  class InputHelper {
    StringTokenizer tokenizer = null;
    private BufferedReader bufferedReader;

    public InputHelper(InputStream inputStream) {
      InputStreamReader inputStreamReader = new InputStreamReader(inputStream);
      bufferedReader = new BufferedReader(inputStreamReader, 16384);
    }

    public String read() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String line = bufferedReader.readLine();
          if (line == null) {
            return null;
          }
          tokenizer = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }

      return tokenizer.nextToken();
    }

    public Integer readInteger() {
      return Integer.parseInt(read());
    }

    public Long readLong() {
      return Long.parseLong(read());
    }
  }
}
