Problem3289--Shifting

3289: Shifting

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
2
Output
2 1
Input
3
Output
1 3 2
Input
4
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]

Source/Category

 
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