You are implementing a simplified collaborative editor sync format. You are given: - An initial document string `doc`. - A list of user *input operations* (keystrokes) applied in order, with the cursor initially at the **start** of `doc`. ### Input operations Each operation is one of: - `append(c)`: insert character `c` at the cursor; cursor moves right by 1. - `backspace()`: delete the character immediately to the **left** of the cursor (if any); cursor moves left by 1 if a deletion happened. - `right()`: move the cursor right by 1 **if** it is not already at the end of the current document. ### Output operations Convert the keystrokes into a compressed list of operations using only: - `insert(s)`: insert string `s` at the cursor; cursor moves right by `len(s)`. - `delete(k)`: delete `k` characters immediately to the **left** of the cursor (equivalent to pressing backspace `k` times). - `skip(k)`: move the cursor right by `k`. ### Goal Return an equivalent list of output operations that reproduces the same final document as the keystrokes, while **compressing** operations by: 1. Merging consecutive `append` keystrokes into a single `insert`. 2. Merging consecutive cursor moves into a single `skip`. 3. Merging consecutive deletions into a single `delete`. 4. Canceling when possible (e.g., an `append` followed by `backspace` should remove the appended character from the output script; a `right` followed later by `backspace` may turn that previously-skipped character into a deletion). ### Examples 1) `doc = ""`, input: `[append('a'), append('b'), append('c')]` Output: `[insert("abc")]` 2) `doc = "aa"`, input: `[right(), backspace()]` Output: `[delete(1)]` 3) `doc = "aa"`, input: `[right()]` Output: `[skip(1)]` Implement a function that performs this conversion. (Assume inputs are such that you only need to handle the behaviors described above; you may ignore any cases not covered by the stated rules.)