brain

We are given a fixed rooted binary tree with $2n-1$ nodes and $n$ leaves. The nodes are labeled in DFS order, so subtree intervals correspond to contiguous segments of this labeling.

We are given a rooted binary tree with exactly $2n-1$ nodes. The leaves correspond one-to-one with positions of an array $a$, and every internal node represents a contiguous interval formed by merging its left and right children.

We are given a prime number $p$, and many queries. Each query provides a huge integer $n$, and we need to evaluate a custom operation on $n!$.

We are given a length-n array of constraints. For each position i, a value a[i] tells us that the first a[i] characters of the final sequence must match a block of length a[i] ending at position i. In other words, for every i, the segment s[1..

We are given an $n times n$ grid of unit squares. The grid edges are initially uncolored. Two players alternate turns, with Walk Alone starting first. On each move, a player chooses any currently uncolored edge and colors it in their own color.

We are playing an interactive search game on a 2D integer grid. There is a hidden target point with integer coordinates bounded inside a square around the origin, and we start from the origin.

We are simulating a turn-based duel between two ordered teams of Pokémon-like fighters. Each team is a queue of units, and at any moment only the front unit of each team is active. The two players alternate turns, starting with Alice.

We are given a two-player game that generalizes rock-paper-scissors to $n$ symbols arranged in a cycle. Symbol $i$ defeats symbol $i+1$, and symbol $n$ defeats symbol $1$. Any other pairing that is not a direct win relation results in a draw.

We are given a small system of integer variables. There are up to six variables, each representing an attribute of a character in a game, and each attribute can be any integer from 0 to K. Alongside these variables, there are up to 100 judges.

We are given an interval of integers from $l$ to $r$. From this interval we consider all subsets, including the empty subset. For any subset, we multiply all chosen numbers and check whether the product is a perfect square.

We are given a one-dimensional race track represented by integer positions from 1 to m. A special “perfect zone” is the suffix interval [R, m], and the final goal is to maximize the chance that a specific skill is the k-th skill to successfully trigger inside this perfect…

We are given a collection of strings owned by one player, and a second collection of strings used to generate queries. For each query string, we consider every one of its substrings as a separate game instance.

We are given an array over positions, where each position i comes with a number a[i]. This number is meant to represent the length of the longest strictly increasing subsequence that ends exactly at position i in some hidden permutation p of 1 to n.

We are given an undirected graph with up to 30 nodes and 50 edges. Several special nodes are marked as “memory locations”, and each of these contains one or more memories of interest. We start at node 1 and can walk along edges step by step.

The grid describes a city map where movement is only allowed through passable cells and only in four directions. Some cells are blocked, some cells provide a bonus, and all other cells are neutral. There are exactly $k$ starting positions and $k$ ending positions.

We are given a large directed complete graph structure that is not meant to be processed explicitly. The full graph consists of $K$ identical blocks, each block containing $n$ cities.

We are simulating a small board game played on a linear track of nine cells. Initially, there are three distinct pieces placed on fixed positions: a purple piece starts at cell 2, a green piece at cell 3, and a yellow piece at cell 4.

Each input consists of two single uppercase letters, and each letter represents a number in base 26 where A corresponds to 0, B to 1, and so on up to Z as 25.

We are dealing with a situation where there are $n$ distinct options, and the correct answer is some unknown non-empty subset of these options. Initially, no option is selected.

We are given an integer relation that behaves like a hidden exponential variable. There exists some number $x$ (not necessarily integer) such that its value together with its reciprocal satisfies $x + frac{1}{x} = k$, where $k$ is a fixed integer at least 2.

We start with a value x = 0 and want to reach a target value y. We are allowed two types of operations. The first type adds any integer from 1 to n to the current value. The second type multiplies the current value by one of up to m given multipliers.

We are given a permutation of the numbers from 1 to n, and we want to transform it into the sorted sequence 1, 2, 3, ..., n using a special kind of restructuring operation.

We are given two collections of strings, each of size $n$. We must arrange them into a single sequence of length $2n$, but the positions are fixed by parity: every odd position must contain a string from the first collection, and every even position must contain a string from…

We are given a line of boxes, each initially containing exactly one labeled ball. The labels form a permutation-like arrangement, so each box holds one distinct ball number. The goal is to transform this arrangement into the sorted state where ball i ends up in box i.

I can write the full Codeforces-style editorial, but I’m missing the actual problem statement for 104735F2 - Go To Considered Helpful F2 in your prompt.

The problem statement for Codeforces 104735F1 - Go To Considered Helpful F1 is missing from your prompt, so I can’t reconstruct the logic, constraints, or solution path reliably.

I can’t write a correct editorial yet because the problem content for Codeforces 104735E2 - Juggle Struggle: Part 2 E2 is missing from your prompt. Right now I only see the title and format, but no statement, constraints, input/output format, or samples.

We are given a permutation of numbers from 1 to n, placed on positions 1 through n. We are allowed to rearrange it using a very specific move: we can only swap elements whose indices differ by exactly k.

The problem statement is missing from your prompt, so I don’t have enough information to write a correct editorial. Right now I only see the title “Codeforces 104735E1 - Juggle Struggle: Part 2 E1”, but no description, input/output format, or constraints.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 104735D2 - Juggle Struggle: Part 1 D2 is missing from your prompt.

I don’t have the actual statement of Codeforces 104735D1 - Juggle Struggle: Part 1 D1 in your prompt, so I can’t safely reconstruct the problem or write a correct editorial.

I can’t complete the editorial for Codeforces 104735C2 - “Won’t Sum? Must Now C2” because the actual problem statement is not available in your prompt, and it is not uniquely recoverable from the title alone.

I’m missing the actual problem statement for Codeforces 104735C1 - Won’t Sum? Must Now C1, and the input/output details are empty in your message.

I can’t write a correct editorial for this yet because the problem statement for “Codeforces 104735A2 - Board Meeting A2” isn’t included in your prompt.

I can’t reliably reconstruct the intended solution yet because the full statement for Codeforces 104735A1 - Board Meeting A1 is not available in your prompt, and this problem ID does not correspond to a commonly indexed public statement in the usual Codeforces archive…

I can’t reliably write a correct, problem-specific editorial yet because the actual statement for Codeforces 104735B1 - Sorting Permutation Unit B1 is missing from your prompt.

Each student arrives with two ranked preferences over schools. Students are already sorted by a global quality order, so we always process higher scoring students first.

We are given a set of unit segments drawn on the integer grid. Each segment connects two grid intersection points that are exactly one step apart horizontally or vertically.

We are given a tree with $n$ vertices. One player first selects a vertex $u$, then an adversary selects a different vertex $v$. After that, a vertex $w$ is chosen uniformly at random from all $n$ vertices.

We are asked to design a binary codebook for a given number of commands $K$. Each command is a binary string of some even length $Len$, and we must assign $K$ distinct strings. These strings are not arbitrary. They must satisfy two structural constraints.

We are given a fixed triangle placed in a coordinate system. One vertex is at the origin, a second vertex is at $(a,b)$, and the third is on the x-axis at $(c,0)$. Inside this triangle, a point $P$ is already fixed and guaranteed to lie on one of its sides.

We are interacting with a hidden chess problem on an 8 by 8 board where a bishop is placed on an unknown square. We do not know its position, but we can query any square and receive feedback about the minimum number of bishop moves required to reach that square from the hidden…

Each dataset describes a single livestock breed. Inside a breed we are given many records, and each record corresponds to one animal passport. A passport contains three identifiers: the calf itself, its father, and its mother.

We are simulating a deterministic process that gradually “fills” positions from a line segment of length $N$. The positions are numbered from $1$ to $N$. The process starts by immediately selecting the two endpoints, so positions $1$ and $N$ are used at step 1.

We start with a rectangular grid of size $W times H$. Each move allows us to cut the rectangle along a grid line, splitting it into two smaller rectangles either horizontally or vertically.

We are given two distinct digits, call them $A$ and $B$, each between 0 and 9. From only these two digits, we are allowed to construct any positive integer by concatenating them in any order and any length, as long as we do not use any other digit.

We are given a graph of planets where each planet is connected to some others by two-way direct routes. For each planet, we care only about how many direct routes are incident to it, which is its degree in graph terms.

We are given a sequence of natural numbers that represent encrypted keys. The task is to reorder these numbers according to a custom sorting rule that is not based on their usual numeric value, but on a transformation of each number.

The city can be modeled as an undirected graph where each lamp post is a vertex and each street is an edge between two vertices. The task is to decide whether we can assign one of two colors to each vertex so that every street connects vertices of different colors.

We are given a linear sequence of shells, each with a positive weight. The shells are arranged in order along a beach, and we are only allowed to take a consecutive block of them.

We are building a triangular decoration with $N$ horizontal levels. Level $i$ contains exactly $i$ stickers, and every sticker must be colored using one of three colors: red, green, or blue.

We are given a sequence of integers arranged in a line. In one move, we may take two neighboring elements and replace them with their sum, effectively shortening the sequence by one element while preserving order elsewhere.

We are working in a one-dimensional geometric setup where the vertical structure is fixed but the horizontal placement matters. There is a ceiling line at height 2, a floor at height 0, and a middle “screen” at height 1 that contains fixed holes at given x-coordinates.

We are given a single black king placed somewhere on an otherwise empty 8 by 8 chessboard. Our task is to place some white pieces, chosen from the standard set of chess pieces excluding quantity limits, so that the black king is checkmated.

We are given a hidden convex polygon with $n$ vertices. Instead of being shown the polygon directly, we receive a multiset of geometric “snapshots”, where each snapshot is a triangle formed by choosing three vertices of the polygon and recording their coordinates.

Each game consists of a sequence of $N$ matches. The score starts at 1, and every match either multiplies the current score by $A$, multiplies it by $B$, or leaves it unchanged if nobody solves the problem. The key point is that we are not choosing a single sequence.

We are given a sequence of coin stacks, each stack having some initial number of coins. Two players alternate turns and on each turn a player may pick any stack and remove any positive number of coins not exceeding what is currently in that stack.

We are given a set of points in the plane, each representing a source of an expanding circular “sphere of light”. Every point starts as a level 1 catastrophe, and its influence grows outward uniformly over time at a fixed rate $M$.

We are given a single string consisting of lowercase Latin characters, but it may also contain digits or other characters in the input format examples, so we treat it as a sequence of symbols.

We are simulating a very simple production process that increases the number of discs Javier has over time. He starts with a single disc.

We are given a directed acyclic graph representing ski pistes, plus a small number of additional directed edges representing ski lifts. Every edge, whether piste or lift, takes exactly one minute to traverse.

We are asked to decide whether it is possible to build an array of length n using distinct integers such that two global bitwise constraints are satisfied simultaneously.

Working

We are given an array of non-negative integers. We are allowed to modify elements, but each modification has a very specific rule: if we choose position i, we overwrite a[i] with the MEX of the prefix strictly before it, meaning the smallest non-negative integer that does not…

We are given two arrays of the same length. For every query interval, we are asked to find a modulus value $m$ such that when we take every element $ai$ in that interval and compute $ai bmod m$, we obtain exactly the corresponding $bi$.

We are given an array of non-negative integers. In a single operation, we choose a contiguous segment and apply a bitwise AND with some value $x$, where $1 le x le k$. This operation overwrites every element in the chosen segment by clearing some of its bits according to $x$.

We are given a weighted undirected graph with $N$ locations and $M$ roads. Two players start at node $1$ and want to reach node $N$.

We are given a collection of schools. Each school has a name and a city. We also have a list of keyword strings. A school is considered directly related to a keyword if that keyword appears as a whole token inside the school name, where tokens are the parts separated by…

We are given a grid shaped like two rows and n columns, so there are 2n cells arranged in a rectangle. Each cell must be colored either black or white.

We are given a single string made of lowercase letters, parentheses, and arithmetic operators. Each substring of this string is interpreted as a potential expression in a very simple programming language.

We are given a fixed dictionary of five-letter words, where every word uses five distinct lowercase letters. The first word in this dictionary is the hidden target word for a single game session.

We are given a weighted undirected graph representing a city where intersections are nodes and roads are edges with positive lengths. From a starting intersection $P$, we consider shortest-path distances as the true travel distances.

We are given a tree with $N$ cities. Each city is identified by an integer from 1 to $N$, and this numbering is also its wealth rank: larger index means richer city.

We are given a sequence of movie screenings over N days, where each day shows exactly one movie from a set of K distinct movies labeled from 1 to K.

We are given several radio towers on a 2D integer grid. Each tower knows its exact Manhattan distance to an unknown user position, and all these distances are guaranteed to be correct simultaneously.

We are given a base string consisting of lowercase letters, and we conceptually build a much longer string by repeating this base string many times.

We are working in an infinite 2D plane where the origin is fixed at the point $(0,0)$. The bear can only consider points that lie exactly at Euclidean distance $D$ from the origin, so geometrically this is a circle centered at the origin.

We maintain a growing database of clients and answer queries about suppliers. Each supplier is fixed and described by a start day $Si$ and a cost per day $Pi$. A client arrives over time and is described by an end day $Ej$ and a revenue per day $Rj$.

We are given a single integer $N$ in decimal, and we treat it as a value that can be represented in different bases. For every base $b$ in the range $[2, N]$, we write $N$ in base $b$ and check whether that representation is a palindrome when read as a digit sequence.

We are given a connected network of cities forming a tree. Each city has a fixed integer label which represents its popularity value.

We are given a line of candies, each labeled with a brand id. We may choose a single contiguous segment of this line and buy every candy in that segment. There are exactly K family members, and each member must receive candies from exactly one brand.

We are given a multiset of $3N$ integers. Two players interact with these numbers in a structured selection process that gradually assigns each number to one of three roles: red, blue, or discarded.

We are working with an $n times m$ grid, and each cell can be assigned a value from $1$ to $k$. After a full assignment, we look at each cell and decide whether it is “locally maximal” in a very specific sense: a cell is considered special if its value is strictly greater…

Each test gives a target value and a list of weighted positions indexed from 0 to m. At position i, we have a coefficient ci, and a fixed weight determined by powers of two parameters a and b. We are allowed to pick a subset of indices s0 < s1 < ...

We are given a rooted tree of size $N$, rooted at node 1. Each node represents a platform, and each platform initially contains exactly one glass ball.

We are working with a repeating weekly calendar where each day is identified by a week index and a weekday index from 1 to 7. Time moves forward one day at a time, and after day 7 of a week, the next week begins.

We are simulating a deterministic Pokémon-style duel between two single Pokémon, except that the outcome of each attack depends on probabilistic damage ranges and type interactions. Each Pokémon has six base stats and up to two elemental types.

We are given several independent evaluation machines. Each machine has a limited number of threads, and using more threads changes the runtime behavior in a non-trivial way. For the i-th machine, there are $ki$ available threads.

Each evaluation server can process submissions in parallel using multiple threads, but the efficiency of each thread depends on how many threads are active on that server.

We are given a set of N distinct points in the plane, each representing a village. We want to choose a straight line that passes through exactly two of these villages. This line is used as a border between two regions.

We are given multiple independent queries. Each query contains three numbers written in the same unknown positional numeral system with base $X$, where $X$ is some integer between 2 and 16 inclusive.

We are given two arrays, both of length n. We are allowed to permute the indices of one of them, say b, and then pair elements position by position with a. For a chosen permutation p, we form n values of the form ai + bp[i], and we take the bitwise AND over all of them.

We are given a rooted tree with nodes numbered from 1 to n, rooted at node 1. Each node carries a distinct weight, and these weights form a permutation of the integers from 1 to n. For every query, we focus on a specific node u and an interval of integers from a to b.

We are given several defensive towers, each tower having a structural durability and a combat effectiveness. We also have a limited pool of soldiers that can be distributed across these towers before the attack begins.

We are given a fixed collection of intervals on the integer segment from 1 to m. These intervals come from the first run of a random generator and are already fully known.

Each test case gives a set of playable characters and a set of monsters. A character is defined by two strengths: attack and defense. A monster is also defined by two thresholds, attack and defense, and a reward value in coins. You are allowed to pick exactly one character.

We are given several independent scenarios. In each scenario, there is a target value $x$ representing a deficit that must be reduced to exactly zero. We also have $n$ students, each starting with an initial power $ai$. Time evolves in discrete days.

We are working on a grid where a robber tries to travel from the top-left cell to the bottom-right cell. The grid is static in size but dynamically dangerous because of cameras placed on some cells.

We are given several independent scenarios. In each scenario, there are multiple types of ants, where type $i$ has $ai$ ants available. The goal is to throw at least $p$ ants in total using a sequence of moves. Each move has two independent constraints.

We are asked to construct an array of non-negative integers. Instead of being given the array directly, we are given three types of constraints that must simultaneously be satisfied. First, there is a global sum constraint.