Canadian Computing Competition: 2025 Stage 1, Senior #5

Wow, your to-do list is empty... but not for long! Over the next few seconds, you'll have to handle $Q$ updates to your to-do list.

For the first type of update, you will have to add a new homework assignment to your to-do list. This assignment will be released at the beginning of second $s$, and will take $t$ seconds to complete $(1\le s,t\le {10}^6)$. For the second type of update you will have to remove the $i$-th homework assignment that was added to your to-do list.

After each update, you wonder: what's the earliest time you can finish all of the homework assignments in your to-do list? You can only work on one assignment at a time, and you must finish a homework assignment once you start it without switching to another assignment.

Input Specification

The first line of input contains an integer $Q$.

The next $Q$ lines each contain a line starting with a character A or D. A line starting with A represents the first type of update and ends with two space-separated encrypted* integers $s^{\prime }$ and $t^{\prime }$ . A line starting with $D$ represents the second type of update and ends with an encrypted integer $i^{\prime }$. It is guaranteed that there have been at least $i$ assignments added and that the $i$-th assignment to be added has not been removed yet.

It is guaranteed that there is at least one homework assignment on your to-do list after every update.

The following table shows how the available $15$ marks are distributed:

Marks	Bounds on $Q$	Additional Constraints
2	$1\le Q\le 3000$	None
6	$1\le Q\le {10}^6$	Only updates of the first type
7	$1\le Q\le {10}^6$	None

*Note that the input for this problem is encrypted. To decrypt and obtain the actual values of $s$, $t$, and $i$, you may use the following formulas:

$s=(s^{\prime }+\text{ans})mod({10}^6+3)t=(t^{\prime }+\text{ans})mod({10}^6+3)i=(i^{\prime }+\text{ans})mod({10}^6+3)$

Here, $\text{ans}$ represents the answer after the previous update and is initially $0$ before any updates. It may also be useful to note that $mod$ corresponds to the $$ operator in most programming languages, indicating the remainder after division. For example, $5mod3=2$ and $17mod4=1$.

Output Specification

Output $Q$ lines, where the $i$-th line contains the earliest time (in seconds) you can finish all of the homework assignments in your to-do list after the $i$-th update.

Sample Input 1

6
A 3 3
A 2 0
A 999996 999995
D 999991
A 1000000 999994
D 999992

Sample Input 1 (Unencrypted)

6
A 3 3
A 7 5
A 4 3
D 1
A 8 2
D 2

Output for Sample Input 1

5
11
13
11
13
9

Explanation of Output for Sample Input 1

The unencrypted sample input is provided for ease of reference.

After the first update, we can start the first assignment at the beginning of second $3$ and finish at the end of second $5$ (interval $[3,5]$).

After the second update, we can do the first assignment over the interval $[3,5]$ and the second assignment over the interval $[7,11]$.

After the third update, we can do the first assignment over the interval $[3,5]$, the third assignment over the interval $[6,8]$, and then the second assignment over the interval $[9,13]$.

After the fourth update, we can do the third assignment over the interval $[4,6]$ and the second assignment over the interval $[7,11]$.

After the fifth update, we can do the third assignment over the interval $[4,6]$, the second assignment over the interval $[7,11]$, and the fourth assignment over the interval $[12,13]$.

After the sixth update, we can do the third assignment over the interval $[4,6]$ and the fourth assignment over the interval $[8,9]$.

Sample Input 2

2
A 1000000 1000000
A 4 4

Sample Input 2 (Unencrypted)

2
A 1000000 1000000
A 1000000 1000000

Output for Sample Input 2

1999999
2999999