|Codeforces Round #176 (Div. 1)|
John Doe has found the beautiful permutation formula.
Let's take permutation p = p1, p2, ..., pn. Let's define transformation f of this permutation:
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.
A single line contains integer n (2 ≤ n ≤ 106).
Print n distinct space-separated integers from 1 to n — a beautiful permutation of size n.
1 3 2
4 2 3 1
A note to the third test sample: