H. Cyclically Coprime
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a single integer $$$n$$$. Please output any permutation $$$p_1, p_2, ..., p_n$$$ such that for all $$$1 \leq i \lt n$$$, $$$p_i$$$ and $$$p_{i + 1}$$$ are coprime. Additionally, $$$p_1$$$ and $$$p_n$$$ must be coprime.

A permutation of length $$$n$$$ is a sequence of $$$n$$$ integers such that all integers between $$$1$$$ and $$$n$$$ inclusive appear in it exactly once.

Two integers are coprime if their greatest common divisor is equal to $$$1$$$.

It can be proven that such a permutation always exists.

Input

The first and only line of input consists of a single integer $$$n$$$ $$$(1 \leq n \leq 2 \cdot 10^5)$$$.

Output

On the first and only line, output $$$n$$$ space-separated integers $$$p_1, p_2, ..., p_n$$$ that satisfy the constraints of the problem.

If there are multiple solutions, you may output any such one.

Examples
Input
5
Output
4 1 2 5 3
Input
2
Output
1 2
Note

In the first sample test case, the output is valid because $$$\gcd(4, 1) = \gcd(1, 2) = \gcd(2, 5) = \gcd(5, 3) = \gcd(4, 3) = 1$$$. There are other valid outputs for $$$n = 5$$$, for example $$$2, 3, 5, 4, 1$$$.