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.math.*;
import java.util.*;

public class Solution {
    public void run() {
        try {
            int n = reader.nextInt();
            int[] p = new int[n << 1];
            for (int i = 0; i < n; ++ i) {
                p[i] = i;
            }
            int offset = 0;
            for (int k = 2; k <= n; ++ k) {
                int i = offset + k * ((n - 1) / k);
                p[offset + n] = p[i];
                for (; i > offset; i -= k) {
                    p[i] = p[i - k];
                }
                offset ++;
            }
            for (int i = 0; i < n; ++ i) {
                writer.print((p[offset + i] + 1) + " ");
            }
            writer.println();
        } catch (IOException ex) {
        }
        writer.close();
    }

    InputReader reader;
    PrintWriter writer;

    Solution() {
        reader = new InputReader();
        writer = new PrintWriter(System.out);
    }

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

}

class InputReader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    InputReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    Integer nextInt() throws IOException {
        return Integer.parseInt(next());
    }
}