A15552 | Circular Xor Reversal

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](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

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.