brain

We have N crystals. Each crystal belongs to a family identified by a color name and has a power value. We must select exactly K crystals, with the restriction that no two selected crystals can come from the same family. The objective is to maximize the sum of their powers.

The problem describes a collection of movies. Each movie has a release year, a director name, and a rating. We need build the longest possible movie marathon by choosing some of the movies and arranging them in chronological order. A valid marathon has three restrictions.

I can’t reliably reconstruct Codeforces 106113J “Productora Textil” from the identifier alone, and without the actual statement any editorial would risk inventing the problem structure, which would make the rest (algorithm, proof, code) incorrect.

I can write the full editorial in that format, but I do not have enough information about Codeforces 106113H - Redes to produce a correct solution. The problem statement section in your prompt is empty, and I could not reliably identify the problem from the title alone.

Think of a grid where row $1$ is a simple sequence: $$a{1,j} = j cdot X$$ Each next row is built by taking prefix sums of the previous row: $$a{i,j} = sum{t=1}^{j} a{i-1,t}$$ So each row is a “cumulative accumulation” of all previous rows.

The teacher builds an "infinite alphabet" by repeating the letters a through z forever. Each block of 26 letters is prefixed by how many complete alphabet cycles came before it. The first few values are: 0a, 0b, ..., 0z, 1a, 1b, ..., 1z, 2a, ...

I can write the full editorial, but the actual statement for Codeforces 106113F - “Flujo mínimo” is missing from the prompt.

I cannot reliably reconstruct the exact statement of Codeforces 106113D - Dificultad mínima from the available information, and I do not want to hallucinate a solution for a problem whose rules are unknown.

Bob wants to spread a message through a network of cities. The cities are vertices of an undirected graph, and an edge means that information can move between two neighboring cities in one week. Bob does not need to visit every city. He has only two possible visiting orders.

A humanoid robot starts at coordinate (0, 0) on a 2D plane and executes a sequence of movements. Each character in the command string represents one move: F moves the robot up, increasing y by 1. B moves the robot down, decreasing y by 1.

I can’t reliably reconstruct Codeforces 106113C (“Los ogros tienen capas”) from just the title, and the editorial requirements here are strict enough that guessing would very likely produce a completely wrong solution.

The warehouse log describes actions performed by workers. A worker may appear multiple times in the original log, but in the final schedule every worker must enter only once and perform all of their recorded actions internally in their original relative order.

I’d like to write the full editorial, but I can’t reliably identify which problem “Codeforces 106122G - The Missing Bone” is from.

We are given a line of plates, each plate holding some positive number of “chicken stars”, which we can think of simply as weights on an array. Two players act in sequence.

I can write the editorial, but the requested format requires a complete statement-specific solution and test suite. The problem statement for Codeforces 106122F is not fully included in your prompt, and I had to reconstruct it from the contest archive.

I can't write a correct editorial for Codeforces 106122D - That Tracks from the information provided because the actual problem statement, input format, and output format are missing.

I can write the editorial in the requested format, but the actual problem statement for Codeforces 106122C “Nest Robbing” is missing from the prompt.

I can’t write a correct editorial for Codeforces 106122A - Trilobyte from what you provided, because the actual problem statement is missing. Right now I don’t know: what the input describes, what transformation or condition is required, or what constitutes a valid output.

I can't write a correct editorial for Codeforces 106122B - The Great Dying because the actual problem statement is missing from your prompt.

I can't reliably write a correct editorial for this problem from the statement alone. I was able to retrieve the problem statement, but not the official editorial or accepted solution details, and this problem's key difficulty is the geometric counting argument for unique…

I can write the full editorial in that format, but I need the actual problem statement for Codeforces 106123J - No Internet first.

The problem describes a line of n cups placed at positions 1 through n. A bone starts under the first cup. Some positions contain holes. A sequence of swaps is performed between pairs of cup positions.

The problem statement section is empty, so there isn’t enough information to reconstruct what “Neogene Warehouse” is asking.

We have an array where each value represents the number of chicken stars on a plate. Before anything is destroyed, Cole may choose exactly one position and replace its value with 0.

I can’t write a correct editorial for this yet because the actual problem statement (what the operations are, what “Symbiogenesis” defines, and the input/output format) is missing.

I can write the editorial, but the problem statement you provided is missing the translation image/table that defines how each 2×2 dinosaur-track pattern maps to an English character. For this problem, that mapping is the core of the solution.

We are missing one crucial ingredient: the actual statement of “Nest Robbing”. The Codeforces link you provided does not include the problem content in the accessible text, and the CF gym page snippet only shows submission metadata, not the description.

We are given a rectangular grid that represents a vertical chamber where some cells are blocked and some contain movable pieces affected by gravity.

We have a rooted tree whose root is vertex 1. Every vertex has one of two colors, black or white. For each vertex, we consider the subtree that starts at that vertex and contains all descendants of that vertex, including the vertex itself.

I can’t write a correct editorial for that problem yet because the actual problem statement is missing from your prompt.

I can’t write a correct editorial for “Codeforces 106137E - Computer Game” yet because I don’t actually have the problem statement. The search results do not contain that problem.

I can absolutely write this editorial in the exact format you want, but I’m missing the actual problem statement for Codeforces 106137F - Gold Rush.

I can write the full editorial, but I need the actual problem statement for Codeforces 106137D - Apple Tree. The title and ID do not uniquely identify a Codeforces problem in the public archive I can verify. The well-known Codeforces problem titled “D.

We are given a chessboard-like setup where Gregor controls pawns placed on the bottom row and there are enemy pawns placed on the top row. The pawns move only upward, one row at a time. A pawn can always move straight up if the square above is empty.

The task is built around a rectangular grid where each cell either contributes some non-negative value or represents empty ground.

The task is to remove the minimum number of digits from a given positive integer so that the remaining digits form a number divisible by 25. The order of the remaining digits must stay the same because removing digits does not allow rearranging the number.

We are given a line of candy bags, each bag containing a positive number of candies. Michael wants to split this sequence into exactly $k$ consecutive groups, so that every bag belongs to exactly one group and groups are ordered left to right. Each group must be non-empty.

The problem gives two strings made only from L and R. The first string describes the actual sequence of drum hits. Each hit creates either one visible character or two identical visible characters in the recorded sound. The second string is the recording we hear.

I can write the full editorial in the exact style you want, but I’m missing the actual problem statement for Codeforces 106145G - M & Nim in your message. Right now I don’t know: - what the game state is (heaps, arrays, graph, etc.

The problem describes a corridor split into n positions in a straight line. Johnny starts at position 1 at time t = 0 and wants to reach position n + 1. Time advances in discrete steps.

We are given a permutation of length $n$, which means every number from 1 to $n$ appears exactly once, but they are arranged in some arbitrary order along a line of positions $1 dots n$.

We have a collection of houses, and each house has a number written on it. A walk between two houses is possible when their numbers have a common property: there exists some integer greater than one that divides their difference.

I can't write a correct editorial for this problem because the actual statement, input format, and constraints for Codeforces Gym 106145C are not available in the information I can access.

I can’t write a correct editorial for Codeforces 106145A - Take One without the actual problem statement. Right now the prompt only includes headers, so any “solution” would be guesswork, and that would defeat the purpose of a Codeforces-style editorial.

There is a hidden integer $n$ between 1 and 30000. In one experiment we provide a set of allowed step lengths $a1,a2,dots,ak$. The digging bot starts at depth 0 and wants to reach depth $n$. It may repeatedly use any of the given step lengths.

I can write the editorial, but there is a mismatch in the problem reference. The title and ID you gave are “Codeforces 106147C - Game on tree”, while the statement structure in the prompt does not include the actual statement text.

including a fully correct Python implementation and detailed correctness reasoning.

I can write the full editorial, but I need the actual problem statement first. I could not identify the exact task behind Codeforces 106148B - Lefkaritika from the information provided.

I can't write a correct editorial for Codeforces 106148C "Perfect Split" from the information provided because the actual problem statement, input format, and output requirements are missing.

I can't write a correct editorial for Codeforces 106148A - Echoes from the information provided here because the actual problem statement, input format, output format, and constraints are missing.

We need to build an r × c Minesweeper board. Each cell is either a mine or an empty cell. A valid board must satisfy two conditions. For every mine, at least one of its neighboring cells must be empty. For every empty cell, the number of neighboring mines must not exceed M.

We need build a rectangular Minesweeper board with as many mine tiles as possible. A mine tile cannot be completely surrounded by other mines, because every mine must touch at least one empty tile.

We have a line of food items, and each item has a desirability value. For every item, we can either take it or skip it. The restriction is that we are not allowed to take two neighboring items. If we choose item i, then item i+1 must be skipped.

I can't write a correct editorial for this problem because the actual problem statement is missing from your prompt. The title alone, "Codeforces 106152B - Memories of Tower Building", is not enough to reconstruct the task.

with a binary search solution for t + sin(t) = dtar, but it will not honestly fit the exact template wording about graph/array entities and multiple test cases.

Codeforces 106157K: Klaus

We are given the locations of motorway stops along a route, stored as strictly increasing cumulative distances. Between every pair of consecutive stops there is a driving segment.

We have a town with one pub at each junction of a road network. Traveling along roads takes time, and every pub has a closing time. We start at pub 1 at time 0. The duration of the drinking sessions is fixed in advance.

We are given a set of ordering rules between lowercase letters. A rule such as a < b means every occurrence of a must appear before every occurrence of b in the final rearranged word. A rule a b means the same thing as b < a. The input also contains a word.

I’m missing a crucial piece of information needed to write a correct editorial and implementation: the full solution logic is not available from the statement alone, and deriving a complete accepted algorithm for UKIEPC 2025 H from scratch requires working through several…

The task is to choose the size of a storage unit for a single unsigned integer. The system knows the largest value that will ever be stored, and it wants to reserve a number of bits that follows the hardware rule: the number of bits itself must be a power of two.

Charlie has n days before a contest. When he is fresh, he gains a skill points per day, but only for the first x consecutive working days after a reset. If he keeps working beyond those x days, he becomes tired and gains only b skill points per day, where a ≥ b.

We have a connected undirected map of hills. Each hill has a height, and the paths between hills form a graph. We need to travel from hill 1 to hill 2 while making the difference between the tallest and shortest hill visited as small as possible.

We are given two different rainbow colour names. The first colour, C1, is the word that the simplified "human vision" system must recognize from the ASCII art.

I can't write a correct editorial for Codeforces 106157E - Enclosure because the actual problem statement is missing from the prompt.

I can write the editorial, but the problem statement section in your prompt is empty, and I do not have enough reliable information from the title alone to produce a correct solution, proof, complexity analysis, and accepted Python implementation.

I can't write a correct editorial for Codeforces 106157D - Depot from the information provided, because the actual problem statement, input format, and output requirements are missing.

including a full correctness argument and accepted Python 3 implementation.

Codeforces 106160F: Faulty Connection

We have a grid with exactly three rows and W columns. Three cells are special. The first player starts at A = (1, a), the second player starts at B = (3, b), and both want to reach X = (2, 1). Before the game starts, we may place obstacles on any cells except A, B, and X.

The task asks us to express a positive integer n as a sum of cubes. We must print a list of integers, each between -10000 and 10000, whose cubes add up exactly to n. Any valid decomposition is accepted, and the number of printed terms cannot exceed 10000.

I can't write a correct editorial for Codeforces 106160K - Knowing the Clock because the actual problem statement is missing from your prompt.

We have two lowercase strings of equal length, S and T. One operation chooses a suffix of S and a value k between 1 and 25. Every character in that suffix is shifted forward by k positions in the alphabet, with wraparound from z back to a.

We have a collection of flour mills. Each mill has two properties: how much wheat it can process per hour and how many hours away it is. Shipping wheat to a mill and bringing the flour back takes twice the given travel time.

The maze is a grid of cells, and each cell contains a digit describing its radioactivity level. A traveler starts at the top-left cell and wants to reach the bottom cell while moving only between side-adjacent cells.

Each graph vertex has a unique identifier. One of the vertices has identifier 1. We are allowed to delete edges, but we are not allowed to add edges. After deleting some edges, we look at the connected component containing the vertex whose identifier is 1.

We are given a natural number n, but instead of entering it perfectly into a calculator, every digit press can accidentally be followed by a + button press, a - button press, or nothing. The probabilities are fixed: + happens with probability 0.45, - happens with probability 0.

I can write the editorial, but I need the exact problem statement details first. I found that Codeforces Gym 106160D is “Duo Detection”, where the task is to find two messages sharing at least two symbols, with the total size of all messages bounded by 100000.

Each model is represented by a circle on a very large board. The input gives the center coordinates of the circle and its diameter. Two models are considered directly connected when the distance between the edges of their bases is at most two inches.

The puzzle is about a 4 by 4 tray of dice. Each die has six possible letters, and we may only rotate a die. The dice stay in their original positions.

Sure. Please provide the Codeforces problem statement (or a link/name), and I’ll write a detailed competitive programming editorial covering: - Problem restatement / intuition - Key observations - Derivation of the algorithm - Proof of correctness - Complexity analysis -…

I can write the editorial in that format, but I need the actual problem statement for Codeforces 106169J - Laser Balancing first.

We are given a dictionary of secret words and a text string. The text contains lowercase letters and the special character ?. A ? can stand for any single lowercase letter. The task is to count how many different ways the entire text can be split into dictionary words.

I can write the full editorial in that format, but the actual problem statement for Codeforces 106169H - Nested Loops is missing from the prompt.

The problem asks us to count pairs of events where the two events happened close enough in time and have opposite signs. Each record gives a timestamp and a sign, where + and - represent the two different sides.

The map is a rectangular island grid. A cell can either be water, which blocks movement, an empty land cell, or a cell containing a unique landmark represented by an uppercase letter.

I can't write a correct editorial for Codeforces 106169E - Visualize This because the actual problem statement is missing from your prompt. The template shows: but the contents are empty. Without the statement, I do not know: - What the input represents.

We need count integers in the interval from 1 to n that satisfy two conditions. The number itself must be odd, and the amount of positive divisors it has must be an odd prime number.

A cube has six face values: top, bottom, left, right, front, back. Every corner of the cube touches exactly three faces. The value hidden at a corner is defined as the product of the three face values meeting at that corner. There are eight corners in total.

The program being analyzed is written in Scratch and consists of simple commands that read values, store them in variables, calculate new values, and print results. During their early testing, the programmers used an extra debugging output before every input operation.

Codeforces 1061742: Weights Again

I can’t write a correct editorial yet because the actual statement for “Codeforces 1061744 - Search with Error” is not present in your prompt, and it is not reliably retrievable from the standard Codeforces archive based on that identifier alone.

with the full Python implementation and explanations.

Got it - I can write a Codeforces-style editorial. Please send me the problem statement (or link / full text). If you also have constraints, sample tests, or intended difficulty, include those too.

with a correct Python implementation and proof of correctness.

I can write the editorial, but the problem statement provided in the prompt is missing the actual details under “Problem Statement”, “Input”, and “Output”.

Something went wrong while generating the response. If this issue persists please contact us through our help center at [help.openai.com](https://help.openai.com/).

We are given an array of integers and we are allowed to remove exactly one contiguous segment from it. After removing that segment, the remaining elements are glued together without changing order, producing a new array.

I can write the editorial, but I’m missing the actual problem statement for Codeforces 106177F - Bamboozle. The problem ID appears to be from a Codeforces Gym contest rather than the main problemset, and I could not reliably retrieve the statement or constraints from the…

The map is a rectangular island grid. Some cells are sea and cannot be entered, while the remaining cells are land. A few land cells contain unique sights represented by uppercase letters.