Circular Xor Reversal
Description
You have an array $a_0, a_1, \ldots, a_{n-1}$ of length $n$. Initially, $a_i = 2^i$ for all $0 \le i \lt n$. Note that array $a$ is zero-indexed.
You want to reverse this array (that is, make $a_i$ equal to $2^{n-1-i}$ for all $0 \le i \lt n$). To do this, you can perform the following operation no more than $250\,000$ times:
- Select an integer $i$ ($0 \le i \lt n$) and replace $a_i$ by $a_i \oplus a_{(i+1)\bmod n}$.
Here, $\oplus$ denotes the bitwise XOR operation.
Your task is to find any sequence of operations that will result in the array $a$ being reversed. It can be shown that under the given constraints, a solution always exists.
The first line contains a single integer $n$ ($2 \le n \le 400$) — the length of the array $a$.
On the first line print one integer $k$ ($0 \le k \le 250\,000$) — the number of operations performed.
On the second line print $k$ integers $i_1,i_2,\ldots,i_k$ ($0 \le i_j \lt n$). Here, $i_j$ should be the integer selected on the $j$-th operation.
Note that you don't need to minimize the number of operations.
Input
The first line contains a single integer $n$ ($2 \le n \le 400$) — the length of the array $a$.
Output
On the first line print one integer $k$ ($0 \le k \le 250\,000$) — the number of operations performed.
On the second line print $k$ integers $i_1,i_2,\ldots,i_k$ ($0 \le i_j \lt n$). Here, $i_j$ should be the integer selected on the $j$-th operation.
Note that you don't need to minimize the number of operations.
2
3
3
1 0 1
9
1 0 1 0 2 1 0 1 0
Note
In the notes, the elements on which the operations are performed are colored red.
In the first test case, array $a$ will change in the following way:
$[1,\color{red}{2}] \rightarrow [\color{red}{1},3] \rightarrow [2,\color{red}{3}] \rightarrow [2,1]$.
In the second test case, array $a$ will change in the following way:
$[1,\color{red}{2},4] \rightarrow [\color{red}{1},6,4] \rightarrow [7,\color{red}{6},4] \rightarrow [\color{red}{7},2,4] \rightarrow [5,2,\color{red}{4}] \rightarrow [5,\color{red}{2},1] \rightarrow [\color{red}{5},3,1] \rightarrow [6,\color{red}{3},1] \rightarrow [\color{red}{6},2,1] \rightarrow [4,2,1]$.