Background

Original link: https://oier.team/problems/X6A。

Problem Description

Arcaea is a music game popular worldwide, well known for its innovative 3D playing interface. In Arcaea, players tap/slide the screen to play the chart along with the rhythm. The scoring rules for one chart play are as follows.

• A chart contains several notes. Each note has one of four judgment results: Perfect Pure, Normal Pure, Far, Lost.
• For a chart with $n$ notes, the base score is $10^7$ points, and the bonus score is $n$ points, so the maximum score is $10^7 + n$ points. Each note is worth $\dfrac{10^7}{n}$ points of base score and $1$ point of bonus score.
• If a note gets a Perfect Pure, the player gets all base score and bonus score of that note.
• If a note gets a Normal Pure, the player gets all base score of that note, but does not get the bonus score.
• If a note gets a Far, the player gets only half of the base score of that note.
• If a note gets a Lost, the player gets no points.
• The play score is the floor of the sum of the points obtained from all notes.

Based on the score, the player also gets a rating.

• If the play score $\geq 9.9\times 10^6$, the rating is EX+.
• If the play score $\geq 9.8\times 10^6$ and $< 9.9\times 10^6$, the rating is EX.
• If the play score $\geq 9.5\times 10^6$ and $< 9.8\times 10^6$, the rating is AA.
• If the play score $\geq 9.2\times 10^6$ and $< 9.5\times 10^6$, the rating is A.
• If the play score $\geq 8.9\times 10^6$ and $< 9.2\times 10^6$, the rating is B.
• If the play score $\geq 8.6\times 10^6$ and $< 8.9\times 10^6$, the rating is C.
• If the play score $< 8.6\times 10^6$, the rating is D.

Now you are given the counts of the four judgment results for a chart play. Please compute the rating for this play.

Input Format

One line with four integers $p_1, p_0, f, l$ separated by spaces, representing the counts of Perfect Pure, Normal Pure, Far, Lost, respectively. The total number of notes is $n = p_1 + p_0 + f + l$.

Output Format

Output a string representing the rating. The seven ratings should be printed as EX+, EX, AA, A, B, C, D, respectively.

44 0 0 0

EX+

33 10 0 1

AA

0 0 0 1

D

Hint

Sample Explanation #1

All notes are judged as Perfect Pure, so the player gets the full base score $10^7$ and all bonus score. Since there are $44$ notes in total, the player additionally gets $44$ points, so the play score is $10{,}000{,}044$. The total score is at least $9.9\times 10^6$, so the rating is EX+.

Sample Explanation #2

The number of notes is $33 + 10 + 0 + 1 = 44$. Among them, $33$ notes are judged as Perfect Pure, $10$ as Normal Pure, and $1$ as Lost. Therefore, the player gets $\dfrac{43}{44} \times 10^7$ base score and $33$ bonus points. The total is $9{,}772{,}760.\dot 2 \dot 7$, and the play score is floored to $9{,}772{,}760$. The total score is at least $9.5\times 10^6$ and less than $9.8\times 10^6$, so the rating is AA.

Constraints

For all data, $p_0, p_1, f, l \geq 0$, and $1 \leq n \leq 100$.

There are $10$ test cases in total. For the first $2$ test cases, $n = 1$ is guaranteed.

Translated by ChatGPT 5