P8223 [WFOI - 02] I wanna moqueve (Shift Sequence).

> It's my fiesta. > > Before one match, kid was defeated on the map of WFOIR1; after one match, kid got up from where he fell. > > kid succeeded; he is no longer who he used to be. Simplified statement: [$\texttt{Link}$](https://www.luogu.com.cn/paste/dlxx9pm0). After finishing this problem, why not go solve [this problem](https://www.luogu.com.cn/problem/P7999) as well?

kid needs to sort a permutation of $1 \sim n$ on a strange computer, and the next save point will only appear later. kid can choose a number $x$. Then, in each subsequent operation, kid may cyclically shift a subarray of length $x$ to the left or to the right (the leftmost / rightmost element moves to the rightmost / leftmost position). The shift amount is $1$. If kid performs more than $23 \times n$ operations, the permutation will explode and kid will fall again. Therefore, please tell kid a way to restore the sequence; leave the remaining operations to €€£!

The input has $2$ lines: The first line contains an integer $n$, representing the length of the sequence. The second line contains $n$ integers, representing the sequence $a$.

The output has $m + 2$ lines. The first two lines each contain one number, which are $x$ and $m$ respectively. $m$ is the number of operations. The next $m$ lines each contain two numbers: the first is the left endpoint of the shifted interval, and the second is the direction, where $0$ means shifting left and $1$ means shifting right. This problem uses $\text{SPJ}$. You will get accepted as long as the cyclic shift operations are correct.

- **Explanation for Sample $1$:** Shift left on interval $(2,3)$, the sequence becomes $2,1,3$. Shift left on interval $(1,2)$, the sequence becomes $1,2,3$. - **Explanation for Sample $2$:** Shift right on interval $(3,5)$, the sequence becomes $4,2,1,3,5$. Shift right on interval $(1,3)$, the sequence becomes $1,4,2,3,5$. Shift left on interval $(2,4)$, the sequence becomes $1,2,3,4,5$. **This problem uses bundled Subtasks.** Subtask ID | Constraints and Notes :-: | :-: **Subtask #0** ($\texttt{1 pts}$) | $n=1$ **Subtask #1** ($\texttt{2 pts}$) | $n=2$ **Subtask #2** ($\texttt{3 pts}$) | $n=3$ **Subtask #3** ($\texttt{4 pts}$) | $n=4$ **Subtask #4** ($\texttt{20 pts}$) | $1 \le n \le 50$ **Subtask #5** ($\texttt{20 pts}$) | $1 \le n \le 100$ **Subtask #6** ($\texttt{50 pts}$) | $1 \le n \le 10^3$ For $100\%$ of the testdata, $1 \le n, a_i \le 10^3$, and the data guarantees that $a$ is a permutation of $1 \sim n$. Translated by ChatGPT 5