John Doe has found the beautiful permutation formula. Let's take permutation p = p 1, p 2, ..., p n . 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 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.

输入描述:

A single line contains integer n (2 ≤ n ≤ 106).

输出描述:

Print n distinct space-separated integers from 1 to n — a beautiful permutation of size n.

备注:

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]