**Description:**
Given an array $a$ of length $n$ and a string $S$ consisting of characters 'L' and 'R'.
- If the character is 'L', we perform one pass of Bubble Sort from left to right.
- If the character is 'R', we perform one pass of Bubble Sort from right to left.
**Task**: Find the minimum prefix length of $S$ required to sort the array $a$. If the array is not sorted even after performing all operations in $S$, output -1.
#### Input
- First line: $n$ ($1 \le n \le 5 \times 10^5$).
- Second line: $n$ integers $a_1, \dots, a_n$.
- Third line: String $S$.
**Constraints:**
- $1 \le n \le 5 \times 10^5$.
- Length of $S$ is at least 1.
- Elements of $a$ are distinct (or rank-equivalent).
#### Output
- Print the minimum number of operations. Output -1 if impossible.
#### Example
Input:
```
5
2 3 4 5 1
LRL
```
Output:
```
2
```
#### Subtasks
- **Subtask 1 (17 points)**: Max 100 inversions.
- **Subtask 2 (18 points)**: $a_i \in \{1, 2\}$.
- **Subtask 3 (25 points)**: String contains only 'L'.
- **Subtask 4 (20 points)**: $n \le 10^5$.
- **Subtask 5 (20 points)**: No additional constraints.
