brain

We are given a very large rectangular grid with n rows and m columns. Some cells are blocked by stones, and all remaining cells are free.

We are given an $n times n$ grid of lowercase letters. This grid is not static: it is overlaid by several independent cyclic “tram rings” that follow nested square paths. Each ring behaves like a circular sequence, and each ring can be rotated independently by any amount.

We are given a dynamic multiset of numbers representing pufferfish sizes. After each update, we are allowed to reorder all values arbitrarily into a permutation.

We are given a multiset of integers and we are allowed to reorder them arbitrarily into a sequence. The goal is to decide whether we can arrange them so that every adjacent pair satisfies a modular relationship: the sum of each consecutive pair, taken modulo M, must equal a…

We are maintaining a dynamic multiset of votes over m participants, each participant identified by an index from 0 to m - 1. Every vote increments the count of one participant, and a removal operation decrements it if that participant currently has at least one vote.

We are given an $n times n$ board where each cell contains some number of stones, and the total number of stones over the whole grid is exactly $n^2$. The target configuration is very rigid: after all operations, every cell must contain exactly one stone.

We are given a rectangular grid and a set of k distinct occupied cells, each containing a labeled slabstone. A rectangular forbidden zone is also given. If any slabstone ends up inside this rectangle at the moment the device is placed, the entire configuration becomes invalid.

We are given a sequence of house prices arranged along a line. The system starts focused on a single “central” house, and over time we expand our attention outward to neighboring houses.

We are given a fixed collection of 10 tasks, each labeled with a difficulty value from the set {1, 2, 3, 4}. The organizer wants to eventually be able to select a set of four tasks, one from each difficulty level.

We are given the final state of an undirected simple graph on $N$ cities. We are told that this graph was not originally built in this form. Instead, it started as a tree on the same $N$ vertices.

We are given a tree and we consider all ways to delete vertices so that the remaining vertices still form a connected subgraph. In a tree, any connected induced vertex set is again a tree, so every valid choice corresponds to picking a connected subtree.

We are given an array of integers, where each value represents the initial attack power of a creature. From this array we can pick any non-empty subsequence, meaning we may choose any subset of indices while keeping their original order.

We start with a list of integers. Two players take turns, beginning with Naya, and each move consists of choosing any two numbers from the current list, removing them, and inserting their greatest common divisor. After exactly N − 1 moves, only one number remains.

We are given a string made only of opening and closing parentheses. The only allowed operation is to take a closing parenthesis from some position and reinsert it anywhere to its left. Opening parentheses are fixed in place.

We are given a tree, meaning there is exactly one simple path between any two nodes. Each query gives us two independent communication requests: one from a to b and another from c to d. Activating a node means that node lies on at least one of the two chosen paths.

We are given a rooted tree where every node carries an integer value. For each query, two nodes are provided and we are asked to consider all nodes that lie on the path from the root down to the lowest common ancestor of those two nodes.

We are given a single string, and we want to break it into contiguous pieces. Each piece is considered valid if its characters can be rearranged to form a palindrome. For every valid way to split the entire string, we assign a score equal to the number of pieces in that split.

We are given one or more sequences of non-negative integers. For each sequence, we want to find the smallest non-negative integer that does not appear anywhere in that sequence. This value is called the MEX, short for “minimum excluded value”.

We are given an initial array of length $N$. After that, a sequence of range updates modifies it: each update picks a segment $[L, R]$ and adds a value $d$ to every element inside that segment. Once all updates are applied, the array is fixed.

We are given a target array of block sums. Each value in this array represents the sum of a contiguous segment of some hidden array $A$, where every segment has fixed length $K$.

Each round of the game is fully described: we know exactly which two cards were played and in which order. What we do not know is which suit was chosen as trump, and that single missing piece affects how every round is evaluated.

We are given a graph of cities connected by undirected roads, all of equal length. Marco starts at city 1 and must reach city 2. Each “day” he walks along a simple walk in the graph consisting of at least 1 and at most K edges, and then stops.

We are given a 1 × N strip where each cell is either water or land. Some water cells already exist, and land cells can optionally be excavated into water by paying a cost per cell. Once we decide what becomes water, we try to place boats.

We are given a tree of $N$ processing units. Each node has an integer label called its frequency. The structure is static, but we must answer many independent queries about communication between two nodes $X$ and $Y$. A message does not travel in a single simple path.

We are given two configurations of stacked blocks distributed across $T$ towers. Each tower is essentially a stack, and every block has a weight.

We are modeling a very small payment system. A customer wants to buy an item priced at $A$ pesos. He pays with a single bill worth $B$ pesos, so the kiosk must return exactly $B - A$ pesos in change.

We are given a tree rooted at node 1. Every node except the root starts with some number of soldiers placed on it. Time evolves in discrete turns.

The city can be seen as a triangular grid of intersections. The first row has one node, the second has two, and so on until the nth row has n nodes. Each intersection is identified by coordinates $(i, j)$, where $i$ is the row and $j$ is the position inside that row.

We are given a tree where each vertex carries a value. We are also given a threshold value c. From all simple paths in the tree, we only care about those paths where the values on the path are not “too extreme” in the sense that the minimum value on the path is at most c and…

We maintain an array of length n that is being modified by three types of global operations, and we are repeatedly asked for range sums.

We are given a sequence of numbers representing a game where two players alternately remove elements from a line.

We are given a fixed array of house heights. Each query paints a contiguous interval of houses. After a painting, we are asked how many “firefighter operations” are needed to extinguish all burning houses in that interval.

We are given an even number of participants, each with a nonzero integer value representing their efficiency. We must pair them up so that every participant is used in exactly one pair.

I can’t write a correct editorial yet because the actual problem statement is missing. Right now the prompt only contains “A” for the statement and empty Input/Output sections, which doesn’t give enough information to determine what the task is (inputs, constraints, or…

I can’t write a correct editorial for this problem yet because the actual problem statement is missing. Right now the only content provided is just the label “E”, with no description of what the input represents, what operations are allowed, or what needs to be computed.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 105806L - “字符串匹配太多了！” is missing from your prompt (it only shows “L” and empty input/output sections).

I can’t reliably reconstruct the problem from just the title and empty statement (“I”) without risking inventing details, and that would make the editorial wrong. Please paste the full problem statement (or a link / screenshot text).

The problem statement you provided is incomplete. Right now it only contains the title “H” with empty input and output sections, so there is no way to reconstruct what the task is actually asking, what the constraints are, or what kind of operations are involved.

I can’t responsibly write a correct Codeforces editorial for “105806F - 排队” because the actual problem content (input format, rules of the queue, and required output) is missing. Right now, only the title is present, and everything else in the statement is blank.

I can’t write a correct editorial for this problem yet because the actual problem statement content is missing. Right now, the only thing provided is the title “二分炼狱”, but there are no definitions of the input, output, or the task itself.

We are given a rooted tree with vertex 0 as the root and vertices 1 through n. Every non-root vertex has exactly one parent, so the structure is already fixed as a rooted tree.

We start with $n$ boxes, each initially containing exactly one ball. We then repeat a reinforcement process $d$ times. In each step, we pick one of the existing balls uniformly at random from the entire system.

The problem statement you pasted is effectively empty (“J”), so there’s no information about the input format, constraints, or what “11 背包” is supposed to mean in this context.

I’m missing the actual problem statement for Codeforces 105806G - Jump Sort (the content section only shows “G” with no description, input/output, or rules).

We are given a geometric defense simulation on a fixed polyline path. A set of balloons appears over time. Each balloon starts at a given arrival time and then moves along a shared piecewise-linear path in the plane at unit speed.

The problem information provided here is incomplete, so a correct editorial cannot be written yet. Right now, the statement only shows a label “M” without any description of the input format, output format, or task definition.

The statement you provided is incomplete. Right now it only contains the title and a single “K”, with no description of the input, output, or task definition.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Codeforces 105806D - 橘猫的背包问题” without any description of the knapsack variant, constraints, or what is being optimized.

We are given a directed graph with n nodes and exactly n − 1 directed edges. Each edge x → y means that the butterfly numbered x considers y its friend.

We are given an array that changes over time, where each change updates a single position. After every update, we must count how many subarrays are “good”.

We are maintaining a security code represented as an array of integers that changes over time. After each change, we need to evaluate a condition based on a fixed list of “favorite numbers” $d1, d2, dots, dD$, where $D le 30$.

We are given a sequence of numbers representing a game where two players alternately remove elements from a line.

We are given a sequence of enemy attack waves. Each wave has two parameters: a damage rate per second and a duration. If the player chooses a level ℓ, every wave is weakened by subtracting ℓ from its damage rate, but never below zero.

We are given a set of circular irrigation sources on a plane. Each source has a fixed position and a fixed watering radius, and it fully covers everything inside or on its circle. Camila wants to place another circle anywhere in the plane.

We are given a sequence of scheduled training sessions. Ideally, there are $n$ sessions, but Vasya may skip some of them. Every skipped session is not lost: it must be compensated later at a future visited session.

The problem gives a weighted graph with a designated starting node. We are allowed to move along edges, and the cost of moving between any two nodes is defined by the shortest path distance in the original graph.

We are given an undirected graph on vertices labeled from 1 to n. The graph has no cycles, so every connected component is a tree, and the whole structure is a forest. Each edge connects two vertices and represents a corridor of energy between two barriers.

The statement you provided is incomplete, so it’s not possible to write a correct, problem-specific Codeforces editorial yet. All we currently know is a single hint: “You can brute force this problem. Simulate what happens if Edward were to drop down at each pole.

The problem is centered around a process that is explicitly described as bubble sort. We are given an array, and the task is to compute some quantity related to how bubble sort operates on that array.

The problem describes a goalkeeping scenario where we are implicitly evaluating how “good” a goalkeeper is under a specific scoring rule applied to a set of situations.

We are given an array and we consider every subsequence formed by deleting any subset of elements while keeping order. For each resulting sequence, we count how many times two adjacent elements are equal. This count is called the number of flashes.

We are given a permutation of length $n$, and we are asked to evaluate a value derived from all of its subarrays using the notion of MEX.

We are given a binary array and we are allowed to rotate it circularly. After choosing a rotation, we compare the original array with this rotated version element by element using XOR. Wherever the two arrays differ, we get a 1 in the resulting array, otherwise we get a 0.

We are given a set of axis-aligned line segments, each representing a neon tube. Every segment is either perfectly horizontal or perfectly vertical.

We are given a list of integers, each representing a “worker” in Zveropolis. For every worker, we must choose a different partner from the same list so that a specific interaction score is maximized.

The problem describes a skier moving down a slope that is divided into discrete lanes. Time progresses in steps, and at each step the skier’s possible positions form a set of lanes. Initially the skier starts in a single lane at the top.

We are given a rectangular solid block made of unit cubes with dimensions $a times b times c$. Every unit cube inside this block has some number of faces exposed on the outside surface, depending on where it sits: corner, edge, face, or fully interior.

We are working with a rectangular grid of size $n times m$, where each cell is considered a vertex of a graph and adjacency is defined implicitly by movement between neighboring cells.

We are given a permutation of numbers from zero to n minus one. For every position i, we want to look strictly to the right and find the first position j where the value becomes smaller than the value at i. If no such position exists, the answer for i is n.

We are given two domino tiles. Each tile has two ends, and each end carries an integer value from 0 to 6. The first domino is described by two numbers, and the second domino is also described by two numbers. We are allowed to rotate each domino, meaning we can swap its two ends.

We are given an array of integers, representing a line of flowers. Each flower has a “color”, but what really matters for the problem is a derived value called saturation, defined as the number of set bits in the binary representation of the color.

The construction starts from a classic Gray code sequence. For each level $n$, we build a permutation $Gn$ of all integers from $0$ to $2^n - 1$. This sequence is then used to define a binary table $Tn$ with $n$ rows and $2^n$ columns.

The problem statement you provided is incomplete (only “I” is shown, with no description of input/output or task).

The statement as provided is incomplete in a way that makes the actual task undefined. All we know is that the input contains a string with characters from {L, R, ?} and that we are allowed to replace every ‘?’ either with ‘L’ or with ‘R’.

We are given an array of integers and asked to extract as many disjoint contiguous segments as possible such that each chosen segment has XOR equal to zero.

We are given a number and allowed to repeatedly modify it using a very specific operation. In one move, we pick any positive integer whose decimal form is made only of the digit 3, such as 3, 33, 333, and so on, and add it to the current value.

I can’t reliably write a correct editorial for this yet because the actual problem content for “Codeforces 106290D - 小丑牌” is missing from your message (the statement section is empty).

I can’t write a correct editorial yet because the actual problem statement for “Codeforces 106272I - Euler” is missing from your prompt.

We are given a line of farmland split into $n$ consecutive plots. Each plot initially contains some amount of wheat.

I don’t have the actual statement of Codeforces 106267B - 排列之差 available in your prompt (the “Input/Output” section is empty), so I can’t reconstruct a correct algorithm or editorial without risking hallucinating the problem.

We are given two very large square matrices $A$ and $B$, but they are not provided in full. Instead, each matrix is described only by its nonzero entries. Every missing position is implicitly zero, and the number of nonzero entries is small compared to $n^2$.

We are given a target image on an $n times m$ grid. Each cell contains either a color label or zero, where zero means transparent.

We are given an array of integers, and we want to determine whether there exists a special value $X$ such that the array can be split into two groups with a very strong number-theoretic relationship to $X$.

We are working with an unknown array of positive integers indexed from 1 to N. A key structural promise is that any two different elements of this array are coprime, so their greatest common divisor is always 1.

We are given an array of integers where both the array values and the modulus values are bounded by 50,000. Each query does not ask for a single computation, but for a nested sum: we pick a segment of the array and then, for every modulus value in a given range, we compute the…

We are given a collection of affine transformations of a single integer variable, all starting from zero. Each operation takes the current value of $x$ and replaces it with $ai x + bi$, where both coefficients are non-negative integers.

The problem statement for “Codeforces 106238I - Heart Lingers, Future Fades” is effectively empty in the input you provided. There is no description of the input format, output format, constraints, or even the computational task itself beyond the title line.

We are given a range of possible outcomes for a hidden integer value $p$, which represents Godflex’s final ranking. We only know that $p$ lies somewhere in an interval $[l, r]$, and nothing more. Alongside this uncertainty, there are several bookmaker offers.

We start with a segment of integers $[l, r]$. At any moment, the process maintains two things: the current segment and a running score initialized to zero. Each round consists of two random choices.

We are given a very small and unusual restriction on the exponent in a power equation of the form $a^n + b^n = c^n$. Unlike classical number theory settings where $n$ is large, here $n$ is guaranteed to be either 0 or 1.

We are given a line of merchants, each holding a single item with a price. The price of the i-th merchant is an integer in the range from 0 to $2^k - 1$, and every price is conceptually stored as a fixed-length k-bit binary number. The system processes three types of operations.

We are given an $n times m$ grid, and we are allowed to choose a single starting cell on the boundary of this grid. From that chosen cell, a process starts that spreads to all four neighboring cells each second, exactly like a breadth-first expansion on a grid.

We are given a sequence of non-negative integers, and we are allowed to optionally apply a digit-reversal operation to any element. Each number can be reversed independently, but only once. After performing these choices, we obtain a final array, and we want to maximize its mex.

We are simulating a process of placing small fixed shapes into a large grid, where the grid behaves like a physical system: cells get filled, whole rows disappear when completely filled, and everything above a removed row collapses downward.

We are given a closed interval of integers from L to R, and we must arrange all these integers into a permutation so that the ordering between any pair of numbers depends entirely on whether they are coprime.

We are simulating a very small programming language that modifies a single integer register $A$, starting from zero. Each instruction either adds a value to $A$ or overwrites $A$ completely with a value.

The building can be thought of as a fixed catalog of rooms distributed across floors, where each floor has a known set of possible room slots and each slot corresponds to one or two actual living places.

We are given a sequence of test cases. Each test case contains a single integer $n$, and for each one we conceptually build an $n times n$ multiplication table where the cell in row $a$ and column $b$ contains the product $a cdot b$.

I can’t reliably write a correct editorial from what you’ve provided because the actual problem statement is missing. Right now I only see the title “Codeforces 106184B - 天才琪露诺与雾之湖的宝藏”, but the input/output and rules are blank.

We are given a square roof with integer coordinates, from $(0,0)$ to $(S,S)$, and a set of hatch positions inside it. We must choose a single point on the roof where a leash is attached.