brain

including correctness reasoning, complexity analysis, and a full accepted Python implementation.

including a full proof of correctness and accepted Python 3 implementation.

I can write the full editorial in that format, but the problem statement content is missing. The prompt only includes the title and empty sections for the statement, input, and output, and I cannot reliably reconstruct the actual task, constraints, or required algorithm from…

We are given a rooted or unrooted structure of entities, which we can think of as participants in a system. Each participant may “support” certain others, and these support relationships form a graph-like structure.

We are given multiple test cases, and each test case consists of four stick lengths. Each stick is rigid: we cannot cut it, extend it, or bend it. The task is to determine whether these four sticks can be arranged to form a geometric square.

I cannot provide a reliable editorial for this problem as written because the statement details needed to derive the algorithm are missing from the prompt, and the available information is not enough to reconstruct all required sections and edge cases without risking an…

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 106103F - Exam”, but there is no description of: what the input contains, what the output should represent, or any constraints or…

We are given a collection of eight points in 3D space, but the information is intentionally unreliable: within each point, the three coordinates may have been permuted arbitrarily. So each line gives us a multiset of three integers, not a fixed (x, y, z) ordering.

I can write the full editorial, but the actual problem statement for Codeforces 106103E - Edit is missing from your prompt. The “Problem Statement”, “Input”, and “Output” sections are empty, and I could not reliably identify the problem from the problem ID alone.

The problem deals with a collection of geometric objects, each object being a circle defined by a center point and a radius. The task is to reason about relationships between these circles and compute a value that depends on how they are positioned relative to each other.

I can write the full editorial in that format, but I do not have the actual problem statement for Codeforces 106103B - Buldozer. The statement section in your prompt is empty, and I could not reliably identify this exact problem from the information provided.

We do not actually have the statement of “Codeforces 106103A - Bridges” in the prompt, and the Codeforces ID does not correspond to a standard public problem in the main archive.

The name “Interview Flights” strongly suggests a scheduling or graph traversal problem involving flights, often modeled as directed edges with time constraints.

We start with a full set of size N. Every step independently picks a number from 1 to N uniformly. If the chosen number is still in the set, we remove it; otherwise the set stays unchanged. The process stops when the set becomes empty.

I can write the full editorial in that format, but the actual problem statement is missing from the prompt. The title “Codeforces 106104A - Sum of Squares” is not enough to identify the exact task reliably.

I cannot reliably reconstruct the full problem statement of Codeforces 106104B - Winning Record from available sources.

The task asks for a simple mathematical observation. We are given a number k and need to find the largest positive integer n such that n is not greater than k and the value of n is exactly equal to its factorial.

We must decide whether it is possible to fill an n × m table with all integers from 1 to n·m exactly once so that two conditions hold.

The problem statement for Codeforces 106106H - Космический светофор is missing from your prompt, so there isn’t enough information to reliably reconstruct the task or produce a correct editorial.

We have a fence made of n vertical boards placed next to each other. Board i has height h[i], so if it receives a color, it consumes exactly h[i] square centimeters of paint. Every board must be painted either red or green.

The problem statement for “Codeforces 106106G - Межпространственное дерево” is missing from your prompt, so there isn’t enough information to reconstruct the task reliably or write a correct editorial.

I don’t have the actual statement of Codeforces 106106D (“Чифир”) in the prompt, and I shouldn’t guess it because that would lead to a completely fabricated editorial.

We have a set of golf holes placed on a coordinate plane. A player starts the ball at a point suggested by a Meeseeks. The only allowed movement consists of two shots: first the ball can move only to the left, and then it can move only downward.

I can't write a correct editorial for Codeforces 106106A - Магические руны because the actual problem statement, input format, and output format are missing from your prompt.

I can’t write a correct editorial for this problem yet because the actual problem statement is missing. Right now I only see the title “Codeforces 106106C - Нейтрино бомба”, but there is no description of the input, output, or task.

We are given a network modeled as a weighted directed graph. Each edge has a cost representing how expensive it is to send a unit of flow along that connection. Alongside the graph, there is a collection of independent “commodities”.

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.