408204: GYM103053 C Time-travelling Fan

Memory Limit:256 MB Time Limit:4 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

C. Time-travelling Fantime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

You are Amelia Watson's diehard fan and want her to earn the most money from SuperChat among all Hololive EN members at all times. As a fan of the time-travelling detective, you naturally learned some of her time-travelling powers as well. However, it turns out that you weren't the only one!

$$$Q$$$ events will occur. Event $$$i$$$ is of the form: "A fan just donated $$$X_i$$$ dollars via SuperChat to Hololive member $$$S_i$$$ at time $$$T_i$$$." After every event, find out the minimum amount you need to spend to ensure that Amelia earns the most money among all Hololive EN members $$$\textbf {at every point in time}$$$ (she is allowed to tie with some of them). You may travel to $$$\textbf {any}$$$ point in time to donate money via SuperChat.

Notes:

- The 5 members of Hololive EN are: Amelia, Calliope, Gura, Ina, and Kiara.

- If $$$T_i = T_j$$$ then events $$$Q_i$$$ and $$$Q_j$$$ would occur simultaneously.

- We recommend using fast input-output functions as the input size is large.

- This problem may require the use of 64-bit integer data types ("long long" in C++)

Input

The first line contains a single integer $$$Q$$$ - the number of events ($$$1 \leq Q \leq 300,000$$$)

Then, $$$Q$$$ lines follow, each consisting of a single name $$$S_i$$$, and two integers $$$X_i$$$ and $$$T_i$$$. ($$$S_i \in$$$ {"Amelia", "Calliope", "Gura", "Ina", "Kiara"}, $$$1 \leq {X_i}, {T_i} \leq 1,000,000,000$$$)

Output

Output $$$Q$$$ integers - the minimum $$$\textbf {total}$$$ amount of money you need to spend to ensure that Amelia earns the most at every point in time after each event.

Scoring

Let $$$Q_{Amelia}$$$ be the number of queries where $$$S_i = $$$"Amelia"

Subtask 1 (13 points): $$$Q \leq 3000$$$

Subtask 2 (8 points): $$$Q_{Amelia} = 0$$$

Subtask 3 (14 points): $$$Q_{Amelia} \leq 5$$$

Subtask 4 (43 points): $$$S_i =$$$ "Amelia" or $$$S_i =$$$ "Kiara"

Subtask 5 (22 points): No additional constraints

ExamplesInput
3
Kiara 50 30
Gura 10 40
Amelia 40 25
Output
50
50
10
Input
10
Amelia 30 25
Gura 20 20
Ina 39 60
Ina 2 1
Kiara 31 23
Amelia 100 100
Calliope 35 300
Gura 204 96
Ina 100 3
Amelia 20 1000000000
Output
0
20
20
20
31
31
31
194
194
194
Note

For the first sample:

Someone time-travelled to $$$T = 30$$$ to give $$$50$$$ dollars to Kiara, so you could travel back to $$$T = 23$$$ and give $$$50$$$ dollars to Amelia to make sure Amelia doesn't earn less than Kiara when Kiara's Superchat arrives.

After that, someone else time-travelled to $$$T = 40$$$ to give $$$10$$$ dollars to Gura at $$$T = 40$$$. However, you have already given $$$50$$$ dollars to Amelia previously, so you do not need to give any more to Amelia as she already earned more than Gura.

Following that, a third person travelled back in time to $$$T = 25$$$ to give $$$40$$$ dollars to Amelia. Because of this, you could travel back in time to $$$T = 23$$$, stop yourself from giving $$$50$$$ dollars to Amelia, and instead only give $$$10$$$ dollars to Amelia to minimize the amount of money you spend.

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