Yuji and his friends are having a jujutsu duel at the dojo. To be able to come up with a fair tournament style, their instructor Satoru has decided to use a ranking system that takes various factors into account such as kicking skill, magic skill, speed, and of course demon slaying skill.

Satoru has a list of all of the students at the dojo, though it is not sorted according to any particular criteria. He would like it to be such that the students are sorted in descending order of demon slaying skill, with ties broken by descending order of magic skill, ties then being broken by descending order of kicking skill, and then ties being broken by descending order of speed, and finally if there are still ties, to break those by ascending lexicographical order of name.

Unfortunately, Satoru's list of students is quite long and he, being a busy jujutsu teacher, has employed your help to sort the list of students according to the above process. Given their stats and names, can you help Satoru out by reporting the names of the students in sorted order?

Umaru's older brother Taihei is off to work again, which means it is time for her to sit back, relax, play some video games, and enjoy delicious snacks including potato chips and cola. Taihei has been trying to teach Umaru the importance of sharing, so to put this into practice, she will be buying bags of chips to distribute to her friends.

The town Umaru lives in can be modeled as a set of $$$N$$$ houses and $$$N - 1$$$ roads such that there is a unique simple (no edges or nodes reused) path between any two houses. Additionally, Umaru has $$$a_i$$$ friends that live in the $$$i$$$-th house. Taihei will be gone for $$$Q$$$ hours, so Umaru plans to go on at most $$$Q$$$ "snack runs". At the $$$i$$$-th point in time (for each $$$i$$$ at most $$$Q$$$), one of two things may happen. The first possibility is that Umaru will go on a snack run. If so, Umaru travels from house $$$u_i$$$ to house $$$v_i$$$ and gives snacks to her friends along the way. If not, she tells her friends to gather at a particular house $$$w_i$$$, in which case the number of friends that live at house $$$w_i$$$ becomes multiplied by a factor of $$$f_i$$$ (these friends come from out of town, friends never leave their houses).

Umaru is having trouble figuring out how many snacks to bring with her on each snack run. Being lazy, she wants to bring the smallest positive integer number of snacks that will be evenly divisible by the number of people in each of the houses that she visits along the way (including her starting city and destination). Given information regarding each of her snack runs, can you help her figure out how many snacks to bring?

Bessie the cow has been kidnapped from Farmer John's farm by the Satellite Girl. She is currently being pulled up to the satellite by a tractor beam which has flipped her upside down. Can you create an artist's depiction of what Bessie currently looks like?

Note that an upside down "^" looks like a "v", an upside down "/" looks like a "\", an upside down "\" looks like a "/", and all other characters are left unchanged. Note that Bessie is entirely upside down, so not only must the characters be flipped as mentioned, but the lines should be output in reverse order as well.

Kaguya has been texting Shirogane a lot recently, but is unsure what his feelings for her are. Can you help analyze Kaguya's text messages to figure out what's going on?

Specifically, Kaguya is convinced that love is war, and that relationships are only built through strategically planned battles. However, in some of her recent texts, she is unsure if some of they have been friendly conversation, or a battle in disguise. For a text message to be a battle, it must contain some yelling — that is, a sequence of 3 or more consecutive 'a's, which can be capitalized in any way.

Help Kaguya identify these hidden battles so she can win the war!

In Attack on Titans, humanity lives in fear of giant humanoid creatures called Titans. In order to defend themselves, the humans built three walls: Wall Maria, Wall Rose, and Wall Sina. Wall Maria is made up of $$$n$$$ separate sections, with the $$$i$$$th section having height $$$m_i$$$. Wall Rose and Wall Sina also have $$$n$$$ sections each, with heights $$$r_i$$$ and $$$s_i$$$ respectively.

Find the tallest section height common to all three walls: the maximum value of $$$h$$$ with $$$h = m_i = r_j = s_k$$$ for some indices $$$1 \leq i,j,k \leq n$$$. Note that for a height $$$h$$$ to be common to all three walls, each wall must have a section of height $$$h$$$, but these sections are not required to be at the same position on all three walls.

Ashley Ketchup is training to be the best dragon collector in the world, and she needs your help.

Whenever she collects a dragon, she keeps them in a small, spherical habitat, known as a "Dragon Ball". Ashley has many of these dragon balls, but she wants to make sure that the dragons she puts in there are always happy. Dragons come in all shapes and sizes, and can be easily intimidated by other dragons. Ashley wants to keep track of the dragons as she adds more to her collection and make sure they are always doing ok. Can you help Ashley?

It's Fantastic Friday, so Izuku Midoriya goes to the local anime trading card dealership to explore the latest releases. He is currently trying to collect the entire "Plus Ultra" card set of anime characters. Unfortunately for him, he does not know how many characters are in this set. He does, however, see that each character has a unique "quirk number."

He has brought his own collection containing $$$N$$$ cards, some of which may be duplicates. His goal is to collect one of each character in a contiguous run of quirk numbers starting at $$$1$$$. More formally, he would like to collect exactly one card each with quirk number $$$1, 2, 3, \ldots K$$$ for some positive integer $$$K$$$. He does not want any duplicates or any extra character cards whose quirk numbers are not part of the contiguous run: this would ruin the collection.

Midoriya cannot bring himself to simply throw a card away; however the card dealership will allow him to trade in any character card he owns for any other card of his choice for $$$A$$$ yen. Midoriya can also buy any character card of his choice outright for $$$B$$$ yen. (It's possible that $$$A \gt B$$$: the card dealer loves anime, but may not be great at economics.) The shop has an unlimited supply of cards of every quirk number. In order to satisfy his wish of possessing a contiguous run of quirk numbers, what is the minimum amount of money Izuku Midoriya needs to spend?

My Hero Academia (you) has taken a break from saving my grades and has now decided to help me with my burgeoning photography hobby. I have taken an image with my camera, but there are a few problems with it. Please help me fix it.

Specifically, I will provide you with my image, represented as a matrix of $$$n \times m$$$ integers. The edges of the matrix "loop around", meaning that the left-most column is considered adjacent to the right-most column, and the top-most row is considered adjacent to the bottom-most row. To fully process the image, we will apply $$$k$$$ transformations sequentially on the image. These transformations will be of the following form (where +x is to the right, +y is up):

• Blur: Given a pixel $$$(i, j)$$$ in the image, replace its value with the average (rounded down to the nearest integer) of its $$$3\times 3$$$ neighboring pixels in the input image (from the original unblurred image), with the edge pixels wrapping around to the opposite side of the image.
• Shift x y: Shift each pixel by $$$x$$$ units horizontally in the +x (right) direction and $$$y$$$ units vertically in the +y direction (up), with the edge pixels wrapping around to the opposite side of the image.
• Sharpen: Given a pixel $$$(i, j)$$$ in the image, if its value is larger than all of its $$$3\times 3$$$ neighboring pixels in the input image (excluding itself, of course), add $$$100$$$ to its value. If its value is less than the minimum value among its $$$3\times 3$$$ neighboring pixels (excluding itself, of course), subtract $$$100$$$ from its value. Again, the edge pixels should wrap around the opposite side of the image when determining neighbors.
• Rotate CW: Rotate the image 90 degrees clockwise.
• Rotate CCW: Rotate the image 90 degrees counter-clockwise.
• Flip Horizontal: Flip the image across the y-axis.
• Flip Vertical: Flip the image across the x-axis.

Given the image and a list of $$$k$$$ operations, please be My Hero Photographia and provide me with the final image.

After years of experimentation, Kakashi has come up with the "square"-jutsu, a powerful technique that strikes lightning onto a large square area of land. Kakashi happens to be testing his jutsu on a mountain, which can be modeled by an $$$N \times N$$$ grid.

Each cell at row $$$1\leq i\leq N$$$ and column $$$1\leq j\leq N$$$ on the mountain has an elevation $$$c_{i, j}$$$. For every cell $$$(i,j)$$$ it is guaranteed that $$$c_{i,j} \leq \min \left(c_{i+1, j}, \space c_{i, j+1}, \space c_{i+1, j+1}\right)$$$ (treating cells outside the $$$N\times N$$$ grid as having infinite elevation). It is also guaranteed that $$$c_{1, 1} = 0$$$.

Kakashi's jutsu is powerful, but limited: square-jutsu can strike any $$$k\times k$$$ square block of mountain cells, but only if the entire $$$k\times k$$$ block lies within the bounds of the mountain grid and only if every cell in the block has elevation within a certain range $$$[a, b]$$$ inclusive ($$$a \leq c_{i, j} \leq b$$$ for all cells $$$(i,j)$$$ in the target square). Given the elevation of every mountain cell and the elevation range allowed by his jutsu, Kakashi wants to know the number of cells in the largest possible square block his jutsu can hit.

To determine the fate of Immanity, Sora and Shiro are playing yet another game!

They are given a string $$$s$$$ of length $$$N$$$ consisting only of lowercase and uppercase English letters. The $$$i$$$th character in has an integer $$$a_i$$$ in the range $$$[1, 100]$$$.

Sora carefully constructs $$$M$$$ (not necessarily distinct) strings, also consisting only of lowercase and uppercase English letters.

Shiro then chooses a (possibly empty) subset of letters from the English alphabet. Let's denote this set as $$$S$$$.

Sora's score $$$k$$$ is calculated through the following process:

• For all characters $$$c$$$ in $$$S$$$, replace all occurrences of $$$c$$$ in $$$s$$$ with a dot ('.'). Note that characters are being replaced, not removed. Denote the new string as $$$t$$$.
• For each character $$$t_i$$$ in $$$t$$$, if $$$t_i$$$ is not equal to a dot, add $$$a_i$$$ to $$$k$$$.
• Each time one of Sora's strings $$$r_i$$$ appears as a susbstring of $$$t$$$, subtract $$$c_i$$$ from $$$k$$$.

Since Shiro wants to beat Sora, she will choose a subset of characters that minimizes Sora's score. You must help her by finding the minimum possible value of Sora's final score, and to also print a string $$$t$$$ which produces this score.

Saitama, the One-Punch Man, is on a mission to defeat a group of monsters in order to challenge the monster boss, Centichoro. The power level of each of the $$$i$$$ monsters is stored in an array, where $$$p_i$$$ denotes the power level of the monster at index $$$i.$$$ Saitama's goal is to defeat the most powerful group of monsters by finding the maximum sum of any contiguous subarray of monster strengths. If he does so, he will be able to fight against Centichoro to save humanity. Help Saitama calculate the sum of the power levels of the corresponding subarray!

Note: The subarray of $$$a$$$ is $$$a$$$ contiguous part of the array $$$a$$$, i.e. the array $$$a_i,a_{i+1}...,a_j$$$ for some $$$1 \leq i \leq j \leq n$$$.

Light Yagami is once again playing games with the detective L. This time, L has invited Light to a fancy restaurant and has brought 3 piles of canned potato chips to the table; unknowingly, this happens to be one of Light's favorite snacks. While waiting for their order, the detective offers a game: Light and L will alternate between taking chips, where each person can take some number of chips $$$1 \leq c_i \leq p_i$$$ from one of the piles i (where $$$p_i$$$ is the number of chips in pile i), or take some number of chips $$$1 \leq c_i \leq \min\{p_i\}$$$ (where $$$\min\{p_i\}$$$ is the minimum amount of chips across all piles) from all three of the piles. Being a gentleman, L offers Light to go first. Is it possible for Light to take the last chip if both play optimally?