A8903. Shifting

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.

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

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

A note to the third test sample:

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