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]
#include <bits/stdc++.h>
using namespace std;
double PI = acos(-1);
double EPS = 1e-7;
int INF = 1000000000;
int MAXINT = 2147483647;
long long INFLL = 1000000000000000000LL;
long long MAXLL = 9223372036854775807LL;
pair<int, int> M[8] = {make_pair(0, 1),  make_pair(1, 0),  make_pair(-1, 0),
                       make_pair(0, -1), make_pair(-1, 1), make_pair(-1, -1),
                       make_pair(1, -1), make_pair(1, 1)};
int ar[2000005];
int main() {
  int n;
  scanf("%d", &n);
  for (int(a) = (1); (a) <= (n); (a)++) {
    ar[a] = a;
  }
  for (int(a) = (2); (a) <= (n); (a)++) {
    int tmp = 0;
    for (int b = 1; b <= n; b += a) {
      swap(tmp, ar[b + a - 2]);
    }
    ar[n + a - 1] = tmp;
  }
  for (int(a) = (1); (a) <= (n); (a)++) {
    printf("%d ", ar[a + n - 1]);
  }
}
