brain

There are $n$ teams, each starting with a fixed strength value. Every pair of teams plays exactly one match, so the tournament is a complete round-robin.

We are given a string made only of opening and closing parentheses. The task is to decide whether this sequence could arise from some valid arithmetic expression after stripping away everything except parentheses.

We are given a collection of story lengths, where each story has a fixed number of pages. Alongside this, we are given several books, each with a page capacity.

We are given an array that is already sorted in non-decreasing order. For each query, we are given a segment of this array, and we are allowed to pick a single integer mask $X$ (with up to 20 bits) and XOR every element in that segment by $X$.

We are given two integers. One is a fixed base-like parameter $k$, and the other is an upper bound $r$. For any non-negative integer $n$, we define a process: if $n$ is divisible by $k$, we divide it by $k$, otherwise we subtract 1.

We are given two strings of equal length and an integer step size $k$. The allowed operation does not let us freely edit characters anywhere. Instead, we can pick two positions whose distance is exactly $k$, and copy the character from one position into the other.

We are given two integers that describe a hidden set of distinct non-negative integers. One of these values is the bitwise OR of all elements in the set, and the other is the bitwise XOR of all elements in the same set.

We are given a graph whose vertices are the integers from 2 up to n. Two vertices are connected by an edge exactly when one of the numbers divides the other.

The game is played on an array of positive integers. Two players alternate turns. On each turn, a player selects a prime number that divides at least one element of the array.

We are given an array of integers, and we are forced to perform exactly one operation: choose a single position and flip the sign of that element. After doing this once, we compute the sum of the entire array and check whether this sum is even.

We are given two numbers that summarize an unknown pair of positive integers. One number represents their sum, and the other represents their difference, where the difference is taken as first minus second. From these two values, we need to reconstruct the original pair.

We are given a large binary table describing how a set of participants answered a large number of questions. Each row corresponds to one participant and each column corresponds to one question. A cell is 1 if the participant got that question correct and 0 otherwise.

We are given a hidden ordering problem where the only way to extract information about relative positions of elements is through a median operation on three indices.

We are given two sequences, each already sorted in non-decreasing order. Both sequences have odd length. The goal is not to reorder them directly, but to repeatedly apply a very specific transformation operation on either sequence until the two sequences become identical.

The task is to construct a permutation of numbers from 1 to n such that when a specific deterministic process called Reversort is applied to it, the total cost of that process is exactly a given value C. If no such permutation exists, we must report impossibility.

The task revolves around constructing an array that produces a prescribed “sorting cost” under a very specific sorting procedure.

We are given a string that represents a sequence of tiles, where each tile is either fixed as a Moon marker, fixed as an Umbrella marker, or unknown. The unknown positions must be filled with one of the two symbols.

We are given a single string representing a sequence of symbols, where each position is either a fixed letter or an unknown placeholder. The fixed letters are two types, think of them as two characters, and the unknowns can be replaced by either of those two characters.

We are given a collection of cards numbered from 1 up to n. For each query, someone chooses a value m and asks for the sum of all card numbers that are divisible by m. In other words, we are summing every multiple of m that appears in the range from 1 to n.

The game consists of a fixed sequence of 98 numbered cards that are drawn one by one from a face-down pile, plus four starting “direction anchors” on the table that define two independent increasing rows and two independent decreasing rows.

We are building a schedule over a line of n days. On each day, we may or may not take two different pills, but with a strict constraint that both pills can never be taken on the same day.

The input describes a network of companies and people where ownership is defined as percentages. Each company distributes 100% of its value among a set of owners, and these owners can be either people or other companies.

We are asked to construct two collections of objects of equal size: notebooks and drawers. Each notebook has two side lengths, and each drawer also has two side lengths.

Working

We are given three strings. We start with a base string s, and we are allowed to take another string t and insert it at any position inside s, including before the first character or after the last one. This produces a new combined string.

We are given a sequence of real numbers that originally came from a very specific construction: someone started with an integer array and then normalized it as if it were a vector.

We are given a collection of strings, all of the same length, over an alphabet of only four characters. Between any two strings we can measure their disagreement by counting how many positions differ, which is just the Hamming distance.

We are given a weighted tree, meaning there are N villages connected by N−1 roads and there is exactly one simple path between any two villages. Each road has a length. On top of this static tree, the king introduces dynamic “security contracts”.

We are given a rooted tree where each node represents a physical segment of a large wooden structure. Each segment has a weight and may split into several child segments at its end.

We are given a set of points in the plane, where each point is a “star” with a fixed creation order from oldest to newest. Initially, every star forms its own cluster. We repeatedly merge clusters until only one remains.

Working

We are given a positive integer $a$. The task is to choose another integer $b$ such that $1 le b < a$, and the expression $$frac{a cdot b}{a + b}$$ is an integer. Equivalently, we need $a cdot b$ to be divisible by $a + b$.

We are given an array of integers and we need to pick exactly three elements from it. The only restriction is structural: if we pick elements at positions $i1 < i2 < i3$, then each consecutive pair must be separated by at least $d$ indices, meaning $i{t+1} - it ge d$.

We are given a sequence of integers indexed from left to right, and we need to choose exactly three positions in this sequence.

We are given a row of pencils, each with a price, and we must end up buying exactly $k$ of them. The process is sequential: we scan from left to right and decide at each position whether to buy that pencil. The cost of buying a pencil is not just its price.

We are given a binary string consisting only of characters 0 and 1. The cost we care about is the number of inversions in this string, where an inversion is any pair of positions i < j such that a 1 appears before a 0.

We are given a binary string, only consisting of zeros and ones. We measure disorder using inversions: every pair of positions where a one appears before a zero contributes one unit.

We are working with two integer intervals. One interval defines all valid values of $x$, and another defines all valid values of $y$.

We are given three integers, each representing a potential side length of a triangle. The task is to determine whether these three lengths can form a valid triangle.

The prompt is missing the actual Problem Statement / Input / Output description for “Codeforces 104688B3 - Prime Time B3”. Without that, I can’t correctly reconstruct the logic, constraints, or solution approach, and any editorial would be guesswork.

I don’t actually have the problem statement here (both the Input and Output sections are empty), so I can’t safely reconstruct Codeforces 104688A2 without guessing the rules.

We are given a circular clock where several hands are visible, but all hands look identical, so we cannot directly tell which one corresponds to hours, minutes, or seconds.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Кубы и квадраты (Cubes and Squares)”, but no definition of the input, what transformation or decision is required, or what the…

We are given a fixed array b that defines how neighboring positions in another array interact through a repeated randomized update process.

We are given a starting integer and a target integer. From the starting value, we can repeatedly apply two transformations. One operation doubles the current number, which in binary corresponds to shifting left and appending a zero bit.

I’m missing the actual problem statement for Codeforces 104692B2 - Roaring Years B2 in your prompt (the “Problem Statement / Input / Output” sections are empty).

I cannot see the statement for Codeforces 104692A2 - Closest Pick A2 in your prompt or in the retrieved context, so I cannot safely reconstruct the exact rules, constraints, or intended solution.

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 104692B1 - Roaring Years B1 is missing from your prompt.

I can write the full editorial, but I’m missing one critical piece: the actual statement of Codeforces 104692A1 - Closest Pick A1. Right now the “Problem Statement / Input / Output” sections are empty in your prompt, so I don’t know: - what the “picks” are (array?

We are given a social network modeled as an undirected graph. Each person has a fixed integer value $pv$, and each friendship has a value $d{u,v}$.

We maintain a dynamic collection of strings that belong to two separate groups: Barbies and Kens. Each update either inserts a string into one of the groups or removes a previously inserted occurrence.

We are given several independent research groups, each with a required threshold value. If a group receives at least its threshold amount of uranium, that group is considered to have reached a “critical state”.

The input describes a program written in a small imperative pseudocode language with nested loops, assignments, input, and output. The structure is block-based: loops can contain other loops, and each loop introduces a new temporary variable that is only valid inside that loop.

We are given a very large grid with height $h$ and width $w$, but only a small number of meaningful cells. Most cells are empty, some contain rocks that block movement, and some contain values that increase the score when the path passes through them.

We are given a weighted undirected network of cities, where each city contains some number of scientists. A scientist can travel along roads between cities, paying the sum of edge costs along their route.

We are given a tree where each vertex represents a nucleus. Every node has two independent attributes, a value that can be thought of as its neutron count and another as its proton count.

We are building a one-dimensional sequence of rooms, each occupying a fixed horizontal segment, but with freedom to place each room vertically inside a constrained interval.

We are given a circular table with $n$ seats and $n$ guests, and each guest comes with a constraint interval $[li, ri]$. This interval describes where that guest is allowed to sit: if we assign guest $i$ to some seat $j$, then it must hold that $li le j le ri$.

We are trying to determine an unknown integer value $p$, which lies in a very large range up to $10^{12}$. We cannot query it directly, but we are allowed two different kinds of interactions. The first interaction is a kind of bounded membership test on $p$.

We are given a line of rooms, each containing some number of employees. Employees can only move between adjacent rooms, and the goal is to gather everyone into a single chosen room.

We are given a sequence of shelves, each shelf containing a fixed number of dolls. A group of children is initially distributed across these shelves, and each second every child standing at a shelf takes one doll from that shelf.

I cannot write a correct editorial yet because the actual problem statement for Codeforces 104702A1 - Minimum Sort A1 is not provided in your prompt, and I do not have enough reliable information to reconstruct it safely. The title alone is not sufficient.

Each visitor behaves like a deterministic clock that starts ticking on their own first visit day. From that moment, they produce an infinite sequence of visits, spaced regularly by their personal period.

Each visitor to Nadja’s site behaves like a periodic event on a timeline. Visitor $i$ first appears on day $ai$, and after that continues to appear every $bi$ days without end. So each visitor generates an infinite sequence of visit days: $ai, ai + bi, ai + 2bi, dots$.

Each day we receive a task, and we must assign it to exactly one of two workers. If we give a task to Arda, we gain value ai, and if we give it to Bimala, we gain bi. The goal is to assign every task while maximizing total gained value.

We are processing a sequence of projects that arrive one after another, and for each project we must immediately decide whether it is handled by Arda or by Bimala.

I don’t have the actual problem statement for “Codeforces 104707B2 - Tower Power (Full)” in your prompt, so I can’t reliably reconstruct the task or derive a correct solution.

I can’t reliably write a correct editorial for this without the actual problem statement. “Codeforces 104707B1 - Tower Power (Subtask)” is referenced, but the input/output format and rules are missing, so any solution I write would be guesswork and very likely wrong.

I don’t have the actual problem statement for “Codeforces 104708D2 - Binary Search Game D2” in your prompt, only the template. Without the rules of the game, the input format, or what needs to be computed, any editorial would be pure guessing and very likely incorrect.

The problem statement is missing from your prompt, so I don’t have the actual rules of the “Binary Search Game D1” to base the editorial on.

I can write the full Codeforces-style editorial, but I don’t have the actual statement of 104708C2 - Fence Design C2 available in your prompt, and I can’t reliably reconstruct it from the title alone without risking inventing details.

The problem statement for “Codeforces 104708C1 - Fence Design C1” is missing from your prompt, so there is no way to correctly derive the algorithm, constraints, or even the intended output format.

The problem statement is missing from your prompt, so there is no concrete definition of what “Square Free B2” is asking, what the input format contains, or what needs to be computed. Without that, any editorial would be guesswork and likely wrong.

The task behind this problem is to decide whether a given integer can be represented as a sum of special building blocks that avoid a particular divisibility structure involving perfect squares.

I don’t have the actual problem statement for Codeforces 104708A1 - Build a Pair A1, so I can’t reliably reconstruct the task, constraints, or solution. Writing a correct editorial without that would be guesswork and would very likely be wrong.

I don’t have the actual statement for Codeforces 104708A2 - Build a Pair A2, so I can’t produce a correct editorial yet. Please paste the full problem statement (input, output, constraints, and samples).

I don’t have the actual statement of Codeforces 104709C2 - Weightlifting C2 in your prompt, so I can’t reliably reconstruct the problem, constraints, or solution.

I couldn’t reliably locate a public statement or editorial for “Codeforces 104709C1 - Weightlifting C1”, and the search results for that gym ID don’t include the problem text itself.

We are given a source string and a target string. The source string can be transformed into the target by processing it left to right, where each character in the source is expanded into either a single copy of itself or two consecutive copies of itself.

We are given a string made of lowercase characters. For every character in this string, we are allowed to either keep it as a single copy or expand it into two consecutive copies of the same character.

I can’t produce a correct editorial yet because the actual problem statement for Codeforces 104709B1 - Equal Sum B1 is missing from your prompt.

The problem statement section is empty, so I don’t have enough information to derive the solution, let alone write a correct editorial.

We are given four values that represent squared distances from the origin to four unknown vertices of a square drawn on the integer grid.

I don’t have the actual statement for Codeforces 104710B2 - Squary B2 in your prompt, so I can’t safely reconstruct the intended problem or derive a correct solution.

The problem statement for Codeforces 104710C1 - Intranets C1 is not included in your message, so I don’t have the actual rules, input format, or task definition needed to write a correct editorial.

I can’t reliably write a correct, problem-specific editorial for Codeforces 104710A2 - Letter Blocks A2 because the actual problem statement (rules, input format, constraints, and required output behavior) is missing from your prompt.

The problem statement section is empty, so there isn’t enough information to derive the solution or write a correct editorial.

I’m missing the actual problem statement for Codeforces 104712D2 - I, O Bot D2, so I can’t produce a correct editorial yet.

I can’t reliably write a correct editorial for “Codeforces 104712D1 - I, O Bot D1” because the actual problem statement is missing.

I can write the full editorial in the exact format you want, but I’m missing the actual problem content for Codeforces 104712C2 - Saving the Jelly C2.

I cannot reliably proceed yet because the actual statement for Codeforces 104712C1 - Saving the Jelly C1 is not available in the prompt, and the codeforces ID does not correspond to a standard publicly indexed problem in my current context.

I can’t reliably write a correct editorial for Codeforces 104712B2 - Pixelated Circle B2 because the problem statement is missing from your prompt.

I’m missing the actual problem statement for Codeforces 104712B1 - Pixelated Circle B1 in your prompt, so I can’t safely reconstruct a correct solution or editorial without risking inventing details.

The problem statement is missing, so I can’t derive the algorithm or write a correct Codeforces-style editorial yet.

The problem statement for “Codeforces 104712A2 - Spiraling Into Control A2” is missing from your message, so there’s no way to reconstruct the intended algorithm or even define the task precisely.

I need to correct something first: I do not actually have the full statement of Codeforces Gym 104712 A1 in the prompt, and I should not guess it from context alone. The content you provided only identifies the problem name but not its rules, input, or required output behavior.

We are given a grid that contains several excavators placed on distinct tiles. Each excavator occupies exactly one cell, and we start with one excavator per occupied cell.

We are given a grid of building blocks, where each block has a roof height. Each block occupies a square region in the plane, and neighboring blocks touch without any gap. A path starts at the center of one roof and ends at the center of another roof.

We are given a sequence of items, each item having a fixed weight. We also have a capacity limit K. The items are considered in a fixed order from 1 to N, and each item is owned by a corresponding gangster. We are not simulating only the real process.

We are given a timeline of H days. On each day k, the police effectively “clear” a prefix of stores, meaning all stores labeled from 1 up to Ck are considered clean on that day. If Ck is zero, no store is clean that day.