brain

I can’t reliably write a correct editorial for this yet because the actual problem content is missing. What you provided only includes the title (“Which Number”) and a tag (“maxsat”), but none of the real statement, constraints, or input/output definition.

I can’t reliably write a correct Codeforces editorial for “106082D - Pseudo Pseudo Random Numbers” from the information provided, because the actual problem statement (inputs, operations, and required output) is missing.

I can’t write a correct editorial without the actual problem statement. Right now, the input/output section is empty, and “Number Maximization” alone isn’t enough to reliably reconstruct the task.

We are managing a line of reactors, each one behaving like a small system with two internal values: a current pressure and a maximum pressure threshold. Initially every reactor has zero pressure, while each position starts with its own threshold value.

We are given a 4 by 4 Latin square over four symbols representing fruits, except that some cells are already empty. The valid full configuration is always a Latin square: every row and every column contains each of the four fruits exactly once.

We are given several independent queries. Each query contains two integers, and we need to decide whether these two numbers form a pair of twin primes.

We are given a polynomial described by its coefficients in increasing order of degree. In other words, the input defines a function F(x) = f0 + f1 x + f2 x^2 + ...

We are working with a graph where the process starts from a single distinguished vertex, initially vertex 1, and we maintain a dynamically growing set of vertices, called $c$. Conceptually, $c$ is always treated as a single “compressed” component.

We are given a long sequence of levels, each level carrying a difficulty value. The player can remove exactly one contiguous block of fixed length $k$, and everything outside that block remains and contributes to the total difficulty.

We are given a rooted tree with vertices labeled from 1 to 2n, rooted at 1. Each vertex represents a “teaching area” that must appear as a connected region inside a grid of size (n+1) by (2n). Each cell of the grid either contains 0 or one of the labels 1 through 2n.

I can write the full Codeforces-style editorial, but I’m missing the actual problem content. Right now, “Codeforces 106467D - Left & Right” in your prompt does not include the statement, constraints, or samples, so I cannot reconstruct the intended solution or guarantee…

We are given a tree, but we do not directly work with edges. Instead, we are given access to its distance matrix, where entry $D{i,j}$ stores the length of the unique path between vertices $i$ and $j$.

We are given an array of non-negative integers. Each query asks about a subarray defined by a range, but the actual range is not given directly.

The task revolves around counting contributions of certain structured binary strings that are implicitly generated by a process that walks along a fixed “main string” and records how far it can match prefixes while extending.

The problem defines a notion of a “level” where movement between tiles follows chess bishop-like behavior, and each pair of tiles has an associated minimum time required to move between them.

A group of N participants wants to visit tourist spots numbered from 1 to K. Each participant comes with a list of places they refuse to visit.

We are asked to count how many different ways we can build a sequence of participants whose individual contributions to a “fun score” add up exactly to a given target value $D$. Each participant contributes either 1 unit of fun in a normal state or 2 units if enhanced by AI.

We are simulating a commuter who travels over a sequence of days, where each day requires access to a bike from one or both of two providers.

We are given a weighted grid. Each cell has a positive value, and we want to select a simple closed shape drawn along grid edges. The shape must not self-intersect and must form a single closed loop. The region enclosed by this loop is a connected set of unit cells.

We are given a construction that starts with a square and then repeatedly places additional squares inside it. Each new square is rotated by 45 degrees relative to the previous one, so the whole picture becomes a nested system of overlapping diagonals and edges rather than a…

We are given a list of positive integers. From this list, we conceptually form every unordered pair of distinct elements. For each pair, we compute the least common multiple of the two numbers, producing a very large multiset of values.

We are given a circular structure with n positions, each carrying a value. A process is defined where we choose a “step size” d, and then repeatedly jump around the circle by adding d modulo n.

We are given an array that is partitioned into consecutive groups of fixed size, and the task is to determine whether the structure can be rearranged into a globally sorted order under constraints that preserve group structure.

We are simulating a process where a snake moves through a fixed sequence of cells over time. At each time step $t$, the head of the snake occupies a known cell $c(t)$. Some cells may repeat over time, meaning the snake can revisit the same position later.

We are given a very small multiset of characters, and we are asked to consider every distinct string that can be formed by rearranging some or all of those characters.

We are given a system that repeatedly manipulates a stack of plates. There are P distinct plates, initially arranged in a stack. Over D days, each day specifies a number Ki.

We are given a sequence of purchase requests, each associated with a cost. Every request must be satisfied exactly once, and satisfying a request corresponds to making one purchase of that item at its full listed price.

We are given a line of spirits standing in a queue, each with an initial height. Two observers look at this queue from opposite ends, but each of them has a very specific visibility rule.

We are given a long uppercase string that represents a recording of a choir performance. Each hamster in the choir has a unique “song”, and each song is exactly two characters long.

We are given two binary grids of the same size, each cell containing a value that can be interpreted as either 0 or 1. The task is to transform the first grid into the second grid using a specific type of operation: choosing a cell (or position) and flipping its value.

We are given a collection of items, each with an integer weight. There is also an initial offset value, which behaves like a starting balance in the system. The process begins from this offset, and each item can be chosen at most once.

We are asked to select exactly k characters from a pool of n, maximizing total strength, but the choice is restricted by two independent classification rules derived from each character’s attributes. Each character has a value ci which we want to maximize in sum.

We are given a system of multiple buildings, each associated with a production rate. Time progresses in discrete days, and as time increases, each building accumulates demand for “food boxes” according to its own rate.

The statement you provided is effectively empty. It only contains the problem title “秘源机兵统御械 - 疾攻” and no description of the input, output, constraints, or rules of the task. A Codeforces editorial depends entirely on those details.

We are given a rectangular grid of size $h times w$. Every cell must be filled with one of three letters: ‘K’, ‘I’, or ‘T’. The counts of these letters are fixed in advance, so the grid is essentially a multiset of characters that must be arranged into a matrix.

We are given a set of points on a triangular lattice defined by two basis vectors, typically denoted $e1$ and $e2$. Every point in the input is expressed as an integer combination $u cdot e1 + v cdot e2$.

We are given two parameters, a value limit m and a window size k. We must construct a sequence a, where each element is between 1 and m, such that a certain process produces different results when the window size is k versus when it is k+1.

We are given 8 teams, and we must arrange them into a fixed single-elimination bracket with 8 seed positions. The bracket structure is completely predetermined: seeds 1 vs 2, 3 vs 4, 5 vs 6, 7 vs 8 in the first round, then winners of (1-2) play winners of (3-4), and winners of…

We are given an array of length $N$, where each position $i$ is associated with a forbidden value $Ai$. The task is to construct a permutation $P$ of numbers $1$ to $N$ such that no position matches its forbidden value, meaning $Pi ne Ai$ for every index $i$.

We are given a set of points on a plane, and the task is to cover all of them using at most two circles. Each circle can be placed anywhere and can have any radius, including zero.

We are given multiple independent queries. Each query provides two prime numbers, both strictly less than 10000, and we treat them as four-digit numbers by padding with leading zeros when necessary.

We are given a long string representing a sequence of enemy types in a game level. Each query selects a contiguous segment of this string, and for that segment we must measure how repetitive its internal substrings can be.

We start with a sequence of non-negative integers. Each move picks two adjacent elements, adds their sum to a running score, and inserts that same sum back into the array between those two elements.

Each item in this problem is a key that has a rigid base length and a single protruding segment somewhere along that base. When a key is placed, its base contributes to a growing horizontal line, because all chosen keys are concatenated in some order without gaps.

We are dealing with three arrays of equal length, representing daily expenses split into food, equipment, and tavern spending. For the original data, every day has the same total spending across all three categories.

We are given a geometric progression defined by its first term and ratio. Concretely, the sequence is A: q, q·r, q·r², q·r³, and so on, continuing infinitely.

We are given a rooted tree of employees. Employee 1 is the root, and every other employee has exactly one direct manager with a smaller index, so the structure is a rooted tree. Each node carries a label, a single lowercase letter representing that employee’s specialty.

We are working on an integer grid where each entity moves in discrete time under two competing forces: player-controlled movement and a deterministic attraction toward the origin.

We are given a permutation of numbers from 1 to n, which we can think of as a sequence placed along a line. For any query segment [l, r], we look only at the values inside that segment and ask for the length of the longest subsequence whose values strictly increase.

The task is not a typical interactive or input-driven problem. Instead, the statement describes a solved Japanese crossword puzzle (a nonogram) that encodes a single hidden picture.

We are given a row of positions, each position holding a stamp labeled with either an opening or closing parenthesis. We do not take substrings in the usual sense. Instead, we build a sequence by walking along these positions.

We are given a prime number $p$ and a string that represents the output of a hidden numeric process applied to an unknown sequence of coefficients $a0, a1, dots, a{n-1}$, where each coefficient is an integer in the range $[0, p-1]$.

I can’t write a correct Codeforces editorial from this yet because the actual problem content is missing. What you provided only includes the title “笨蛋题” and no description, input format, output format, or constraints.

The problem content you provided only contains the title and no actual statement, input format, output format, or constraints.

The problem statement is effectively missing here. What you provided only contains the title, with no input/output description, constraints, or sample behavior to anchor a solution.

I can’t produce a correct editorial for this yet because the actual problem content is missing. Right now, “Codeforces 106384D - 繁星坠海” is provided without any statement, constraints, input/output description, or samples.

We are given a string of length $n$, where each position represents a light bulb colored red, green, or blue. The only operation available is to pick a bulb and “touch” it, which immediately resets its color to one of the three colors uniformly at random, independently of…

Codeforces 106289D: Cube

Codeforces 106270B: Boulevard of Broken Cars

We are asked to build a fixed logic circuit over $n$ input nodes. Each input node carries one of four symbols: three colored signals $R, G, B$, and a special transparent signal $$ that behaves like an “empty” value.

We are given a nearly complete undirected graph on $n$ cities. Originally, every pair of cities had a road, so the graph was a clique. Then a small number of edges, at most 200, were removed.

We are given a sorted list of distinct points on a number line. The task is to cover all these points using at most $k$ segments, where a segment can be any interval $[a,b]$ and its cost is its geometric length $ A useful way to reframe the problem is to think of grouping points.

We are working with a tree where every node is either normal or special. A walk is allowed to move along edges freely, but there is one asymmetry in how nodes behave during the walk: normal nodes can be revisited any number of times, while each special node can appear at most…

We are given a graph whose vertices are points on a plane, but the geometry only matters through the x-coordinates. Each edge connects two vertices, and an edge can be thought of as a straight segment, although crossings between segments do not allow traversal.

We are given points placed on a circle, each point having an angle θ and an independent probability p of being “activated”. After activation, every triple of activated points forms a triangle, and all such triangles together act as a defensive region.

The grid describes a city map where each cell is either free ground, an obstacle building, a street tile, or one of two special positions: the starting point and the target.

We are asked to construct three non-empty strings over lowercase English letters such that the pairwise distances between them match three given integers.

We are given an array of integers. We are allowed to repeatedly apply a specific local operation on any adjacent pair. The operation takes two neighboring values, computes the bitwise AND of the pair, and then XORs that value into both elements.

We are given a rectangular grid made of two colors, represented by . and . This grid is not arbitrary; it is assumed to be a fragment of a much larger infinite tiling. The hypothesized structure is a chessboard-like arrangement of identical square blocks.

We are given a rectangular floor plan made of small square rooms arranged in an r by c grid. Between adjacent rooms there are walls, and each wall has a digit cost indicating how expensive it is to drill a pipe through that boundary.

We are given a tree with $n$ vertices. Each edge must be assigned a color from a palette $0$ to $K-1$, where $K$ is not fixed in advance and is part of what we are trying to maximize. Once edges are colored, we look at simple paths in the tree.

We are given a hall with $d$ doors. Exactly one door hides a prize, and all others are empty. The player is allowed to initially choose a group of $s$ doors instead of just one.

Each card type comes with a collection of buy and sell offers, each tied to a specific price level. A buy offer at price p means someone is willing to purchase at any market price up to p.

We are simulating a very specific construction process that builds a permutation indirectly. Instead of being given the final arrangement of cards, we are told how the deck is built step by step, and we are asked to reverse engineer the decisions that would produce a desired…

We are dealing with a hidden structure on a set of $N$ labeled crewmates. Each crewmate secretly points to exactly one other crewmate, and every crewmate is pointed to by exactly one person.

We are given a target state of a simplified snooker-like scoring system. At any moment, there are two players, and one of them is currently at the table. We know the current scores of Player A and Player B, we know how many balls remain on the table, and we know whose turn it is.

We are given a motion process that starts from an unknown integer position $X$. From this starting point, a sequence of moves is executed.

We are given a collection of axis-aligned rectangles placed on a 2D plane, each representing a window. Every window also has a unique height value, which determines visibility: if two windows overlap, the one with higher height covers the other in the overlapping region.

We are given two teams, each consisting of all athletes whose skill values form a contiguous integer segment. Monland has skills from $lM$ to $rM$, and Berland has skills from $lB$ to $rB$. One special athlete from Monland, the one with skill $lM$, is fixed as Monocarp.

We are given a string composed of lowercase Latin letters. The task is to cut this string into several contiguous segments so that every character belongs to exactly one segment. Each segment must satisfy a strict structural constraint.

We are working with a lineup of n soldiers. Each soldier is associated with two assignments: one for the morning formation and one for the evening formation. Each assignment is a number between 1 and n representing a rifle type, except some entries are unknown and marked as −1.

We are interacting with a hidden geometric shape centered at the origin. In each test case, the hidden object is either a circle or a square, both centered at $(0,0)$, and we can only probe it by asking whether specific integer lattice points lie inside it.

We are given a single probability value p, describing the success rate of one independent attempt to obtain a required result. A student has exactly three independent attempts. Each attempt either succeeds with probability p or fails with probability 1 - p.

We are given a collection of parent-child relations written in the form “A, son of B”. Each statement says that person A has a single known father B.

We are given a directed network of gears connected by shafts. Each shaft transfers torque from one gear to another, but only a fraction of the incoming torque survives, determined by an efficiency percentage on that shaft.

We are asked to construct a permutation of the numbers from 1 to n. From this permutation we look at two classical subsequence measures: the length of the longest strictly increasing subsequence and the length of the longest strictly decreasing subsequence.

We are interacting with a hidden permutation of length $n$, and our only way to learn about it is to submit test permutations of the same length. Each query gives a score equal to how many positions match the hidden permutation exactly.

We are given a directed graph where vertices represent train stations and edges represent one-way train connections. Two people start from two different stations, and each can travel along directed edges any number of times.

We are given a simple orthogonal polygon, meaning its boundary is a closed cycle made only of horizontal and vertical segments, with no self-intersections. The vertices are listed in counterclockwise order, so walking through them traces the city boundary.

We are given a row of $n$ holes, each containing some number of stones. The process we simulate is a repeated game played $t$ times. In each game, a single “hand” starts at hole 1 carrying exactly one stone and moves strictly from left to right.

We are given a sequence of musical notes, each represented as an integer pitch. We are also given a fixed vocal range, defined by an inclusive interval from ℓ to h.

Two players are about to perform a single exchange based on sealed bids. One player, Old MacDonald, has already hidden a number of coins in a cup, and you know exactly how many coins that is, call it $c$. You also have $n$ coins available.

We are given a set of points in the plane that represent checkpoints of a race route, but the order in which the runner visited them is lost.

We are simulating a driver moving through a sequence of road signs, where each sign either sets a specific speed limit or removes the current restriction and restores the original national speed limit.

We are given a hidden permutation on positions $1 ldots N$. This permutation defines how a binary string of length $N$ is transformed: each step simply reorders the bits according to the permutation.

We are given a set of accounts. Each account already comes with two numbers: how many people it follows, and how many people follow it.

We are given a single integer s, and we need to split it into two integers a and b such that their sum equals s. Both a and b must be nonzero, and both must lie within the range of three-digit integers, meaning between −999 and 999 inclusive.

We are given a list of gadget prices and an initial amount of money. The buying rule is restrictive: before purchasing any gadget, the current amount of money must be at least ten times the price of that gadget. After buying it, the money is reduced by the gadget’s price.

We are given three arrays of length n. The first two arrays define the boundary of an n by n grid. The first column is filled directly from the array a, the first row is filled from the array b, and the top-left cell is shared between them.

We are given a rooted tree where vertex 1 is the root, and every other vertex has a fixed parent. On this tree we consider permutations of the vertices, meaning every vertex label from 1 to n appears exactly once in some order.