Shifting

2000ms

262144K

Description:

John Doe has found the beautiful permutation formula.

Let's take permutation p = p₁, p₂, ..., p_n. Let's define transformation f of this permutation:

$\text{[math]}$

where k (k > 1) is an integer, the transformation parameter, r is such maximum integer that rk ≤ n. If rk = n, then elements p_rk + 1, p_rk + 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.

Sample Input:

Sample Output:

2 1

Sample Input:

Sample Output:

1 3 2

Sample Input:

Sample 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]

Informação

Provedor Codeforces

Código CF286B