brain

The problem statement is missing from what you provided. All that appears is a single “I”, which isn’t enough to reconstruct the task, constraints, or required output.

I’m missing the actual problem statement for Codeforces 106139H - Prime Segments. Right now the prompt only contains the title and an “H”, but no definition of the input, output, or task, so there’s no way to reconstruct the algorithm correctly or write a meaningful…

I can’t write a correct Codeforces editorial from just “G” without the actual problem statement. Right now the input/output and constraints are missing, so any solution would be guesswork and would likely describe the wrong problem entirely.

The statement for Codeforces 106139F - Mod is missing from your prompt (only the title and empty I/O sections are provided).

I don’t have the actual statement for “Codeforces 106139E - Matrix Construction” in your prompt (it’s effectively empty), so I can’t reliably reconstruct the intended problem or write a correct editorial without risking inventing details.

I can’t reliably write a correct, problem-specific Codeforces editorial here because the actual statement of “106139B - Cut ellipse” is missing from your prompt (it only shows placeholders for input/output and no geometry description).

I can’t reliably write a correct editorial for “Codeforces 106139A - Customized Shortest Path” from what you provided, because the actual problem statement (graph definition, what “customized” means, constraints, and query format) is missing.

We are tracking a very unusual climb. Instead of a single position moving up a staircase, we have four distinguishable paws of a cat, each sitting on integer steps. The cat starts with all four paws at position 0, and wants to end with all four paws at position n.

We are given two sequences of the same length. One sequence represents Morty’s grades over n days, the other represents Rick’s grades over the same days. Each grade is an integer from 0 to 5, where 0 is a special value meaning absence.

Each input object is a convex polygon described not by vertices but by its directed edges in counterclockwise order.

We are given an array of distinct strengths representing gorillas positioned in a line. A segment $[l, r]$ is considered valid if the two strongest gorillas inside that segment sit exactly at the ends of the segment, meaning no interior element is larger than either endpoint.

We are given a row of independent rotors. Each rotor stores a value that wraps around, so rotor i behaves like a number on a circle from 0 to mi - 1. The system starts with every rotor at zero, and we want to reach a target configuration b.

Label the birdhouses by their positions $P_1,\dots,P_n$ in the plane, with all pairwise distances distinct.

The allowed tool is a straightedge together with the ability to construct a line parallel to a given line at a fixed distance equal to the ruler width.

We are given an $n times n$ grid where each cell is already colored either red, blue, or white. White cells are flexible, we are allowed to repaint each of them independently into either red or blue. Blue and red cells that are already fixed must stay unchanged.

We are given a grid of free and blocked cells, and we need to count how many distinct closed robot routes exist. The robot always starts on a free cell, moves to any of the 8 neighboring cells (including diagonals), and forms a cycle that returns to the starting cell.

We are given two fixed side lengths of a triangle, $a$ and $b$, and we want to understand what integer values a third side $c$ can take so that the three segments form a valid triangle with positive area.

We are working with a line of $n$ cells. Starting from an empty state, we perform $n-1$ painting operations. In operation $i$, we choose any contiguous segment of the line and repaint all cells in that segment with color $i$, overwriting anything previously painted.

We are observing a traffic light that cycles through four phases in a fixed order. The light starts at red, then switches to yellow, then green, then yellow again, and finally returns to red, repeating this cycle forever.

We are given an array of integers and a threshold value $d$. After we optionally delete exactly one contiguous segment from the array, the remaining elements must form a sequence whose maximum value minus minimum value is at most $d$.

We are given a hidden permutation of length $n$. Only two special elements matter: the position where the smallest value $1$ sits, and the position where the largest value $n$ sits.

We are given all integers from 1 to n, each written on exactly one card, and these cards are arranged into a single sequence using a fixed construction rule.

Please go ahead and provide the Kvant problem statement you want solved.

We are maintaining a graph that starts empty and evolves through a sequence of edge insertions. Each inserted edge has one of two colors, red or blue, but the underlying connectivity of the graph ignores colors.

We are given a binary string representing a line of battlefield cells. Each cell is either empty or contains an enemy. The goal is to eliminate every enemy using two kinds of actions. A lightning strike removes exactly one chosen enemy.

We are given a positive integer n whose decimal representation contains no zeros. From this number, we define a family of transformations: a “cyclic shift” where each operation moves the last digit of the number to the front.

We are given a tree where every vertex carries a color label. The task is to repeatedly delete parts of the tree until nothing remains, but deletions are constrained in a specific way. In one move, we may choose any set of colors and remove all vertices of those colors at once.

We are given a grid representing a road with obstacles, where each cell is either empty or blocked. A vertical car of fixed height k initially sits in the first column, occupying rows from 1 to k.

We are given a tower composed of horizontal layers. Each layer contains three positions, and each position may either still have a block or already be removed. The input represents these layers in a staggered textual form, but conceptually each row is just a triple of cells.

We are given an array that can shrink under two very specific deletion rules. The first rule allows us to remove a single occurrence of the smallest value currently present in the array, and when several positions contain that minimum value, we are free to choose which one…

We are given a sequence of points in the plane, and the order of these points is fixed. From this sequence we want to pick a contiguous segment, say from index l to r, and check whether the polygon formed by visiting these points in order is a strictly convex polygon when…

Let $A = a_n a_{n-1}\ldots a_0$ in decimal.

We are given an array of integers. For any integer, we define a digit function that takes its decimal digits, computes their bitwise XOR, and returns the result. For example, for 507 we compute 5 ⊕ 0 ⊕ 7, which gives 2. Let this function be g(x).

We are given a sequence of measurements over time, stored in an array. Each query asks us to look at a contiguous segment of this array. The twist is that every segment length is not arbitrary, it is always one of two fixed lengths, either L1 or L2.

We are given a set of targets, each target has two parameters: a base energy cost and a fatigue factor. The athlete may choose any subset of these targets and decide the order in which to hit them.

We are given a directed graph where each vertex represents a room in a mansion and each directed edge represents a one-way door between rooms. Every door has a cost of either 0 or 1 depending on whether it is already unlocked or requires using a badge to pass through.

We are given a day that starts at time 0 and ends at time T. Inside this interval, there are N scheduled presentations, each occupying a half-open segment [si, ei), meaning it starts at si and ends just before ei. These presentations may overlap or be disjoint.

We are given an array of integers for each test case and we are asked to pick two distinct elements and evaluate an expression formed from them.

We are given an array of numbers and asked to choose a subsequence that maximizes the variance of its elements. Variance, in this context, measures how spread out the selected values are around their mean, so we want a subsequence whose values are as far apart as possible.

We are given a rectangular board of size $n times m$. We also have rectangular blocks of size $a times b$. The task is to determine how many such blocks can be placed on the board if they are aligned to the grid and cannot overlap, and crucially, they cannot be rotated.

We are given five integers per test case, each representing how many times a specific letter or component is available.

We are given a balanced bracket string of length $n = 2^k$. The only allowed transformation is applied at a chosen scale $m = 2^x$. We partition the string into consecutive blocks of size $m$, and inside each block we split it into two halves of equal size.

We are working with a rooted tree where the root is fixed at vertex 1. Each edge has a weight that behaves like a “popularity” value. A walk always starts at the root and repeatedly descends until it reaches a leaf.

We are given a string of digits arranged in a circle, and we are allowed to rotate it any number of times. Each rotation is one cyclic shift either left or right.

We are given several simple convex polygons drawn on a plane, with the special property that any two polygons either do not touch at all or one lies completely inside the other. There is no partial overlap and no edge crossings between different polygons.

We are asked to compute how many diamond blocks are needed to construct a stepped pyramid of height $N$. The structure is layered: level $i$ (starting from 1 at the top) is a square whose side length is $2i+1$, so it contains $(2i+1)^2$ blocks.

We are given a tree of size $N$, where each node represents a game. Each game $j$ comes with a range of followers $[Lj, Rj]$ and a value $Kj$. If a follower $k$ plays game $j$, they gain $Kj$ aura.

We are given a rectangular grid with $N$ rows and $M$ columns, initially completely empty. Two players alternate turns. Wilson always plays first, and on his move he marks any currently empty cell with a W. Pedro responds on his move by marking any empty cell with a P.

We are given an undirected graph where vertices represent cards and edges represent mutual trust relationships between pairs of cards.

We are maintaining a growing collection of stacks, where both the number of stacks and their contents evolve over time. Initially there are no stacks. The system processes a sequence of operations in order. One operation creates a new empty stack and appends it to the end.

We are given a long race consisting of n laps, where each lap has exactly one winner among 26 possible drivers, labeled by lowercase English letters. So a full race is simply a string of length n over an alphabet of size 26.

We are given a single numeric string that represents two concatenated integers, A and B. These two numbers originally come from an address format where A and B are separate components, but in the message they have been glued together without any delimiter.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Meeting for Meals”, but there are no details about the input, output, constraints, or rules of the problem.

We are given a collection of identical-length segments placed on the non-negative integer line. Each segment starts at some integer coordinate and covers exactly L consecutive integer points. So a segment starting at position l covers all points from l to l + L − 1.

Each test case gives a collection of papers, and each paper is evaluated by a small group of reviewers. Every reviewer assigns an integer score between −3 and 3, and the paper’s total score is just the sum of these values.

We are designing a small maze, at most 8 by 8 cells, where each cell contains one of four directional arrows. A token starts at the top-left cell and repeatedly follows a deterministic process until it first reaches the bottom-right cell. Each step has two phases.

We start with the integers from 1 to n, each appearing once. In one move, we pick some non-empty subset of the current numbers and delete it, but the chosen subset must have a very specific property: the greatest common divisor of all numbers inside it must be exactly k.

There are two independent queues of people waiting on opposite riverbanks. Each person becomes eligible to board a boat only after their individual arrival time.

We are looking at a partially observed snooker frame. At the moment Panda turns on the TV, the table is in some intermediate configuration: a number of balls remain on the table, and both players already have some accumulated scores.

We are given a circular arrangement of villages, where each village has a single crop type. A valid “cut” means splitting the circle into two non-empty connected parts.

We are given a tree with $n$ nodes, and for each node we know its degree in the tree. Then every degree is decreased by one, so each value $d[i]$ now represents $deg(i) - 1$.

We are dealing with a single-line queue of $N$ people, numbered implicitly from the front (position 1) to the back (position $N$). Two specific people in this line are Alice and Bob, but their exact positions are not directly given. Instead, we are told two relative observations.

We are working on a grid-like experiment where laser energy accumulates as it travels through space. Each receiver sits at a fixed coordinate and contributes a fixed bonus if we choose it as the endpoint of a laser run.

We are given a rectangular grid whose vertices contain coins. The grid has $R times C$ lattice points, and a ball starts on one of these lattice points at $(M, N)$.

We are given a string made only of the characters I, C, and P. From this string, we repeatedly want to form the pattern “ICPC” by selecting four positions whose characters match I, then C, then P, then C, in that order in the original string.

We are given a sequence of festival stalls arranged in a fixed order. Each stall has two attributes: the number of people Jack would meet if he enters it, and the happiness he gains from entering it.

We are given a directed graph where each edge represents a street between two cities. Every street has two attributes: a travel time and a required pass level. If Elena owns a pass of level $P$, she is allowed to use only those streets whose requirement is at most $P$.

We are asked to construct a representation of an integer $X$ using a fixed prefix of natural numbers starting from 1. For some chosen length $N$, we take the sequence $1, 2, 3, dots, N$ and assign each number either a plus or minus sign. The resulting signed sum must equal $X$.

We are given a permutation of the numbers from 1 to N, representing books arranged on a shelf. Over M rounds, a fixed operation is performed, but in each round Jack is free to choose which book to remove (as long as it is not currently the rightmost book).

We are given a directed graph where intersections are nodes and footpaths are weighted directed edges. Each edge has a travel time and also a set of visible colors. A navigation system works in a peculiar way: at any intersection, it displays a single color.

We are given a grid of uppercase letters. The task is to find the smallest axis-aligned rectangle such that inside that rectangle there is at least one occurrence of each of the five letters W, A, L, D, and O.

We are given a collection of closed time intervals representing meetings. Each meeting occupies a segment on a number line, and two meetings are considered compatible for merging if their time intervals overlap in the sense that they share at least one point, including endpoints.

We are given a circular line of n positions, where each position holds a value between 1 and m. We are also given a deterministic update rule f that takes three consecutive values on this circle and produces the next-day value for the middle position.

We are given a start point and an end point in the plane, and between them lies a sequence of vertical “gate positions” at strictly increasing x-coordinates.

We are given a route that always moves forward through cities in a fixed order from city 1 to city n. Between every consecutive pair of cities i and i+1 there are several alternative roads, each with two properties: a travel time and a maximum supported vehicle weight.

We are given a line of $n$ seats arranged in a row, indexed from 1 to $n$. A group of people arrives one by one and each person must choose a seat. The rule is that every new person always sits in a position that maximizes their distance to the nearest already occupied seat.

We are given a single string that represents the name of some entity, such as a person, country, or organization. From this name, we must construct a new word that describes the “entering action” for that entity using a fixed linguistic rule.

We are given a line of GPUs, each starting with a fixed load. We are allowed to modify each GPU independently by adding an integer adjustment, but each adjustment is capped in magnitude by a common value $k$.

We are given a rectangular grid of size $N times M$, where each cell can be painted with one of $K$ colors. The twist is that the rectangle is not used as a flat sheet. One of the lengthwise sides is rotated before gluing, producing a Möbius band.

We are given a rectangular grid of cells. The outer boundary is a solid wall except for two openings: one at the top-left cell and one at the bottom-right cell, which act as the start and end points.

We are given multiple queries, each describing a continuous segment of house numbers from $A$ to $B$. Every house number has an associated value called its key, defined as the largest odd divisor of that number.

We are given a system of locations called hubs. From any hub, a daily move consists of two independent choices: first we leave the current hub using a “departure form” of some methodology, then we enter a destination hub using an “onboarding form” of some (possibly…

We start with a potion whose initial value is 1. We then apply a sequence of exactly n rune operations, where each operation is either rune A or rune B. Each rune multiplies the current potion value by a fixed integer factor, but those factors are unknown to us.

We are given a simple polygon described by its vertices in cyclic order. The polygon is guaranteed not to self-intersect, so its boundary forms a clean closed shape.

We are given two players who each receive the same number of cards from a standard deck. The cards are already fixed for both players, but only Eve is allowed to reorder her cards freely before the game starts.

We are given an initial amount of money and a fixed number of years. Each year, we are allowed to hold a multiset of bonds. Each bond type has a purchase cost and produces a fixed yearly profit.

We are given a language over lowercase letters where some short patterns are forbidden as substrings. Any string that contains at least one forbidden pattern is considered invalid and removed from the language.

We are given a sequence of pre-booked taxi rides in a city where travel happens on a grid. Each ride has a fixed start time and a start and end coordinate.

We are given a simple polygon in the plane, described by its vertices in order, and a family of infinitely many parallel straight lines representing a bamboo forest. These lines are equally spaced, and each line has the same inclination given by an angle θ.

I cannot reliably reconstruct Codeforces 106184A from the information currently available. The statement for “秘术「天文密葬法」” is not present in the prompt, and the web results only show contest metadata without the actual problem definition or input/output rules.

I can’t write a correct editorial from that input because the actual problem content is missing. Right now I only see the title “Codeforces 106184C - 天才琪露诺与克劳恩皮丝” but the statement, constraints, and samples are not provided.

We are given a circle of $2n$ seats. Each seat initially holds a labeled item, and labels repeat, with the guarantee that every label appears an even number of times. The seats are arranged so that each position $i$ has a unique opposite position $i+n$ on the circle.

We are given a tree of $n$ planets. Each planet is connected to its parent by exactly one bidirectional space route, and each route has a deadline. The route can be used only if, at the moment you start traversing it, your current time is not greater than its deadline.

We are given a line of plates, each holding either an apple (a) or a banana (b). We start from an initial configuration and want to transform it into a target configuration using a sequence of operations, but the operations are not arbitrary single swaps.

We are given a timeline starting from today, where today is fixed as Monday. The calendar then proceeds day by day, and we want to count how many of the next m days are working days. Two types of restrictions define non-working days.

We are given a string $s$. The task is to construct a different string $t$ such that two conditions hold simultaneously: the beginning of $t$ matches the entire string $s$, and the end of $t$ also matches the entire string $s$.

We are working in a 3D coordinate system that is not the standard Cartesian one but a triangular lattice embedding, where points are represented by integer triples.

We are simulating a laser beam fired from the origin that travels through a vertically stratified atmosphere. The space is divided into horizontal layers stacked by height, and each layer has its own propagation speed for the beam.

We are given a target value $n$, and we want to represent it as a sum of chosen building blocks. Each building block has a “power”, and we have an unlimited supply of blocks whose powers are exactly the prime numbers, with the special rule that 1 is also considered prime.

We are given a path graph on $n$ vertices, where every vertex $i$ is connected to $i+1$. On top of this structure, an extra hidden edge $(a, b)$ has been added, with the promise that there is at least one vertex strictly between them, meaning $a + 2 le b$.