2424\. Longest Uploaded Prefix

Medium

You are given a stream of `n` videos, each represented by a **distinct** number from `1` to `n` that you need to "upload" to a server. You need to implement a data structure that calculates the length of the **longest uploaded prefix** at various points in the upload process.

We consider `i` to be an uploaded prefix if all videos in the range `1` to `i` (**inclusive**) have been uploaded to the server. The longest uploaded prefix is the **maximum** value of `i` that satisfies this definition.  
  
Implement the `LUPrefix` class:

*   `LUPrefix(int n)` Initializes the object for a stream of `n` videos.
*   `void upload(int video)` Uploads `video` to the server.
*   `int longest()` Returns the length of the **longest uploaded prefix** defined above.

**Example 1:**

**Input**

["LUPrefix", "upload", "longest", "upload", "longest", "upload", "longest"]

[[4], [3], [], [1], [], [2], []]

**Output:** [null, null, 0, null, 1, null, 3]

**Explanation:**

    LUPrefix server = new LUPrefix(4); // Initialize a stream of 4 videos.
    server.upload(3); // Upload video 3.
    server.longest(); // Since video 1 has not been uploaded yet, there is no prefix.
                      // So, we return 0.
    server.upload(1); // Upload video 1.
    server.longest(); // The prefix [1] is the longest uploaded prefix, so we return 1.
    server.upload(2); // Upload video 2.
    server.longest(); // The prefix [1,2,3] is the longest uploaded prefix, so we return 3. 

**Constraints:**

*   <code>1 <= n <= 10<sup>5</sup></code>
*   `1 <= video <= n`
*   All values of `video` are **distinct**.
*   At most <code>2 * 10<sup>5</sup></code> calls **in total** will be made to `upload` and `longest`.
*   At least one call will be made to `longest`.