## USACO 2022 January Contest, Gold

## Problem 2. Farm Updates

Contest has ended.

**Log in to allow submissions in analysis mode**

Due to the dynamic nature of the economy, Farmer John needs to make changes to his farms according to a series of $Q$ update operations ($0\le Q\le 2\cdot 10^5$). Update operations come in three possible forms:

- (D x) Deactivate an active farm $x$, so it no longer produces milk.
- (A x y) Add a road between two active farms $x$ and $y$.
- (R e) Remove the $e$th road that was previously added ($e = 1$ is the first road that was added).

A farm $x$ that is actively producing milk, or that can reach another active farm via a series of roads, is called a "relevant" farm. For each farm $x$, please calculate the maximum $i$ ($0\le i\le Q$) such that $x$ is relevant after the $i$-th update.

#### INPUT FORMAT (input arrives from the terminal / stdin):

The first line of input contains $N$ and $Q$. The next $Q$ lines each contain an update of one of the following forms:D x A x y R e

It is guaranteed that for updates of type R, $e$ is at most the number of roads that have been added so far, and no two updates of type R have the same value of $e$.

#### OUTPUT FORMAT (print output to the terminal / stdout):

Please output $N$ lines, each containing an integer in the range $0\ldots Q$.#### SAMPLE INPUT:

5 9 A 1 2 A 2 3 D 1 D 3 A 2 4 D 2 R 2 R 1 R 3

#### SAMPLE OUTPUT:

7 8 6 9 9

In this example, roads are removed in the order $(2,3), (1,2), (2,4)$.

- Farm $1$ is relevant just before $(1,2)$ is removed.
- Farm $2$ is relevant just before $(2,4)$ is removed.
- Farm $3$ is relevant just before $(2,3)$ is removed.
- Farms $4$ and $5$ are still active after all queries. Therefore they both stay relevant, and the output for both should be $Q$.

#### SCORING:

- Tests 2 through 5 satisfy $N\le 10^3$, $Q\le 2\cdot 10^3$
- Test cases 6 through 20 satisfy no additional constraints.

Problem credits: Benjamin Qi