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.

Input

A single line contains integer $*n*$ ($2 ≤ *n* ≤ 10^{6}$).

Output

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

Note

A note to the third test sample:

• $*f*([1, 2, 3, 4], 2) = [2, 1, 4, 3]$
• $*f*([2, 1, 4, 3], 3) = [1, 4, 2, 3]$
• $*f*([1, 4, 2, 3], 4) = [4, 2, 3, 1]$