brain

We are given a set of points on a 2D plane. Each point represents a “city”, and the task is to compute the length of the shortest possible route that starts at some city, visits every city exactly once, and returns to the starting city.

We are given a string that is built from two kinds of characters, where one of them acts like a structural marker and the other forms a repeating pattern.

We are given a grid with $k$ rows and $n$ columns. Each cell may or may not contain a mineral. Instead of observing the grid directly, we are given the output of a scanner.

We are given two extremely large integers $l$ and $r$, written as decimal strings, and we need to count how many integers in the inclusive range $[l, r]$ satisfy a special digit property. A number is considered valid when the product of all its decimal digits is a prime number.

We are working on a rectangular grid with coordinates increasing to the right and upward. The piece starts at the bottom-left cell, which is $(1,1)$, and the goal is to reach the top-right cell $(n,m)$.

We start with a sequence of blocks placed in a line, each block having a fixed height. Initially every block is its own segment.

We are controlling a chariot moving on an infinite integer grid. The starting state is fixed at the origin, and each second we choose a direction for the chariot.

We are given a word written in a very restricted alphabet consisting only of the characters O and K. This word is not meant to be processed directly as text. Instead, it must be translated into a sequence of symbols from a pseudo-Morse system that only uses two characters: .

The grid is partially partitioned by black cells into horizontal and vertical segments. Every white cell belongs to exactly one maximal horizontal segment and exactly one maximal vertical segment. Each such segment has a prescribed sum, given in the input.

We are given several disks drawn on a plane. Each disk is a filled circle, defined by a center point and a radius. The disks act like regions that become dangerous, and we are interested in the geometry of the remaining safe space.

We are given a collection of N objects, each object representing a paper. Every paper contains a list of references to other papers, forming a directed graph where an arrow goes from a paper to each paper it cites.

We are given a sequence of names representing votes in an election. Each line corresponds to one vote for a candidate, and each candidate is identified by a single uppercase string. The task is to determine which candidate received strictly more votes than every other candidate.

We are given a one-dimensional stage of length R, where valid positions run from 0 to R. A group of dancers exists, but we never see their initial positions. We only know that every dancer repeatedly applies the same sequence of horizontal moves.

We are given a collection of rooms connected over time by corridors that appear and disappear. Each corridor becomes available at a specific hour and remains usable for a fixed duration of $M$ hours, after which it vanishes.

We are given a set of N distinct lattice points on a huge integer grid. These points are mandatory: they must appear as vertices of a simple polygon we construct.

We are given a line of towers, each positioned at integer coordinates from left to right, with a height assigned to every position. All heights are distinct, so there is a unique tallest tower.

We are given a collection of gifts, each with a preferred “ideal” delivery day. For every gift, we must choose an actual delivery day. That chosen day is not allowed to be earlier than its ideal day, but it can be later.

We are given a sequence of numbers representing the current “power balance” between two armies arranged in pairs. Each position contributes an integer value, and that value can change over time in a uniform way across the entire array. Two operations happen online.

We are given two strings, a source string $S$ and a target string $T$. Lusius wants to transmit a shortened version of $S$ using a very unusual compression rule: any substring of $S$ can be replaced by a special wildcard character .

We are given a very large rectangular grid of size $w times h$. A snake of fixed length $k$ must be placed in a “straightened” form, meaning it occupies exactly $k$ consecutive cells either horizontally in one row or vertically in one column.

We are given a tree that is built incrementally. The first district is the center of the city, and every next district is attached to one previously built district, so the structure is always a rooted tree with node 1 as the root. Each district has a population value.

We are asked to count pairs of distinct integers $a$ and $b$ with $1 le a < b le n$, such that the pair has exactly two common divisors. The only numbers that are guaranteed to divide both $a$ and $b$ are the divisors of their greatest common divisor.

We are given two ordered collections of target points on a line: one set lies strictly to the right of the origin and the other strictly to the left. A robot starts at position 0 and must visit every point in both sets.

We are given a string of length $n$, representing a poster already filled with uppercase Latin letters. The task is to modify this string so that the substring “NEIMARK” appears as many times as possible, while balancing a cost model: changing any character costs 1 unit of…

Two objects move strictly to the right on a number line. The human starts one meter ahead of the robot and moves with constant speed v1 meters per second, meaning after t seconds the human has advanced exactly t · v1 meters beyond its initial offset.

We are given a sequence of diploma levels and a sequence of prize types, and we must count how many consistent ways exist to assign prizes to participants grouped by diploma level. There are $m$ diploma categories.

We are simulating a sequential distribution process over a fixed number of people. There are $m+1$ participants in total: one special participant, the intern, and $m$ identical regular employees. A list of $n$ gifts arrives in order, each gift carrying a positive value.

We are given a multiset of stick lengths. Each stick can be used exactly as a full side of a quadrilateral. From these sticks we want to count how many distinct isosceles trapezoids can be formed. A valid trapezoid uses exactly four chosen sticks.

We are given a multiset of integers that are claimed to be divisors of several hidden numbers. Each hidden number belongs to a different employee.

We are given a single integer $n$. The task is to split $n$ into a sum of positive integers, where every summand must avoid a specific forbidden set: powers of two.

We are given a fixed number of candies and a fixed number of employees. Each employee must receive either exactly 2 candies or exactly 3 candies. If an employee receives 3 candies, they are considered happy; otherwise, they receive 2 candies and are not happy.

We are given several independent test cases. In each test case there is an array of card values and a parameter $k$.

We are given a tree where every vertex carries a numeric label. From this tree, we consider any simple path between two vertices. Once a path is fixed, it forms a linear sequence of node values in the order they appear along that path.

We are given a set of n friends sitting at a party, each of whom has a uniquely preferred drink. Kaz assigns each friend exactly one drink, forming a permutation of size n. Some friends may immediately receive their correct drink, while others do not.

We are given a vertical stack of rectangular blocks. Each block has a fixed weight proportional to its width and a fixed horizontal position interval $[li, ri]$. The blocks are placed one above another in order, and each block must support everything above it without tipping.

We need to construct a set of $n$ distinct lattice points in a bounded square so that a very specific geometric rule induces a permutation-like behavior. Each point $Xi$ looks at all other points and selects its nearest neighbor.

We are given a sequence of positive integers and we want to count how many non-empty subsequences are “safe” in the sense that they never contain a triple of elements that can form a triangle.

We are maintaining a family of n sets indexed from 1 to n. Every set starts identical and contains only the number 0. Over time, we apply range updates.

We are given a string whose full structure is indirectly encoded through its Z-function. The Z-array at position i tells us how far the prefix of the string matches the substring starting at i, so it captures all prefix overlap information in a compressed form.

We are given five fixed points on the plane, each with integer coordinates, and we are allowed to connect them with straight line segments.

We are given a permutation of the numbers from 1 to n. For any segment of this permutation, we can build its Cartesian tree, where the root is always the maximum element of that segment, and the left and right children are defined recursively by splitting the segment around…

We are given a rectangular grid where each cell contains a lowercase letter. A valid object to count is a simple path of exactly 13 distinct cells connected by edges in the grid, moving only up, down, left, or right.

We are given an array of positions, each position must eventually be assigned either an opening bracket or a closing bracket. Each choice has its own cost per position: placing an opening bracket at index i costs a[i], while placing a closing bracket costs b[i].

We are given a single “group” of $n$ cells, similar to one row, column, or box in Sudoku. Each cell contains a set of candidate numbers, and we are guaranteed that there exists a valid way to assign exactly one number per cell such that all chosen numbers are distinct.

We are given a small set of programming contest problems, and for each problem we know how long each of three teammates would need to implement it if they are the one assigned to it. A value of -1 means that a particular teammate is unable to implement that problem at all.

We are working with a fixed railway network of 426 stations. The connections between stations are also fixed across all test cases, and each station is identified by a string name.

We are given an array of integers, each quite large and chosen independently at random. From these numbers we are allowed to keep some and discard others. Every kept number must be assigned to exactly one of three labeled groups, A, B, or C.

We are given a set of polygonal “tiles”. Each tile is a piece of a unit square that was repeatedly cut by straight lines, so the original object was a square and every cut was a straight segment crossing it.

Each round of the game presents a state of your current capital and an integer chosen by the judge. That integer is drawn uniformly from the range from 1 up to your current money, so larger balances immediately increase the range of possible outcomes for that round.

We are given an $n times n$ grid of cells, and we must assign a color to every cell. The coloring is constrained in two ways. First, each color is allowed to appear only a limited number of times globally, at most 150 cells per color.

We start with a clean permutation where the array is initially a[i] = i. Each operation performs a swap between two positions, and after a sequence of such swaps the array becomes a time-evolving permutation of 1..n.

We are working with a tree where every vertex initially holds its own index as its value. Over time, the values change because we repeatedly pick a path between two vertices and add a number to every value along that path.

We are given a hidden collection of binary strings, each of fixed length 50. There are n of these strings, but they are not revealed directly.

We are given a complete set of pairwise “distances” between up to ten unknown points in three-dimensional space. These values are not exact Euclidean distances. Each true geometric distance has been perturbed independently by a small random value in the interval $[-0.1, 0.

We are given a stream of intervals, and after each new interval arrives we must answer a planning question: using only the intervals seen so far, what is the largest number of them that can be chosen so that none overlap in time.

We are asked to construct a small neural network-like gadget that behaves like modular addition over a prime modulus $p$.

We start with a collection of $n$ singleton sets, where set $i$ initially contains only the element $i$. After that, we process $q$ operations.

We are given a set of n sparse “cards”, each of length m. Each card has letters written only at some positions, while all other positions are blank. We also have a target string s of length m. We are allowed to stack all cards in some order from top to bottom.

The statement you provided is not usable in its current form, so I can’t write a correct editorial without guessing.

I can’t write a correct editorial for this problem as given because the actual problem statement is missing. Right now we only have the title “Игра с тайным смыслом” and empty input/output sections, which isn’t enough to reconstruct what the task is…

I can’t reliably write a correct editorial for this yet because the actual problem statement for Codeforces 105700B - “Родные просторы” is missing from your message.

We are given an undirected connected graph where every edge has a nonnegative weight. A “journey” is any walk starting from node 1 and ending at node k that is not allowed to reuse the same edge twice, though revisiting vertices is fine.

We are given a sequence of trees placed along a straight line. Each tree has a fixed position and a height. A tree can either remain standing as a single point or be cut and fall entirely either to the left or to the right, turning into a segment whose length is determined by…

I can’t reliably write a correct Codeforces editorial from this prompt because the actual problem statement is missing.

The problem statement as provided is not readable enough to reconstruct the task. The input and output sections are effectively empty, and the only visible fragment (“A H 5·10³ O V 5·10¹⁰”) does not preserve enough structure to determine what is being asked.

We are building sequences of length $n$, where each position holds a value from $1$ to $m$. The twist is that we are given a growing list of interval constraints.

We are given a sequence of signed integers that behaves like a properly nested structure, similar to a multi-type bracket system.

We are given several test cases, each containing an array of integers. For each array, we are allowed to reorder its elements arbitrarily. After reordering, we compute a derived value at every position, defined as the value placed there minus its position index.

We start with a binary string that always has a very rigid structure: some prefix of zeros followed by a suffix of ones. The parameter $m$ determines how many ones appear at the end, so the string is fully determined by a single number rather than arbitrary bit patterns.

We are given a fixed integer a1 and a length n. We need to count how many sequences of positive integers a2, a3, ...

Two regular polygons share the same center, one placed above the other. The top polygon can freely rotate while the bottom polygon stays fixed. Because the top shape hides part of the bottom one, only the uncovered region of the bottom is paintable at any moment.

We are given a string made only of the characters a, b, and c. The string is guaranteed to have no two equal characters next to each other, and all three characters appear at least once somewhere in the string.

We are given a rooted tree with vertex 1 as the root. Each vertex carries a numeric value and also a unique rank. The task is not about arbitrary paths in the tree, but about very specific paths constrained by ancestry and by rank filtering.

We are asked to take a string and split it into contiguous pieces. Every piece must read the same forwards and backwards, so each segment is a palindrome.

We are given an array of integers, and we repeatedly apply two types of operations. The first operation is simple: pick any position with a positive value and reduce it by one.

We are asked to build a permutation of the numbers from 1 to n. For each position i, we compare the value placed there with its index and take the absolute difference. This produces a multiset of n values.

We are given a tree where every node already has a color, and a desired final color for each node. We are allowed to repaint a node any number in the range from 1 to N, and each repaint counts as one operation.

We are tracking a set of cars moving along a straight line. Each car starts at position zero and moves with a constant speed during any query interval. However, the speeds are not fixed globally, they can change over time due to updates.

We are given a directed acyclic graph where each city is a node and each road is a directed edge. Traveling along a road costs money, but unlike standard shortest path problems, the cost of each road is not fixed.

We are given a process that runs for exactly $X$ minutes. At the start, a light bulb is on. Each minute, Joe must either toggle the bulb or enter a sleeping phase that lasts exactly $L$ minutes. During sleep, nothing happens to the bulb, and the clock still advances normally.

We are given an array of integers and asked to examine every contiguous subarray of length at least two. For each such subarray, we compute a value based on its size and its two smallest elements.

The task describes a very simple production process: each glass of mixed fruit juice consumes exactly one mango and one orange.

We are given a line with two types of points: villages at fixed integer coordinates and monsters at other integer coordinates. Monsters can move freely along the line, but their movement is blocked by walls that we may construct.

We are given a collection of items, each item has a fixed weight and a hidden “true value” that we ultimately care about.

We are given a sequence of class days and a collection of news events, where each event is active over a contiguous range of days.

We are given a line of buildings, each with a height, and a starting position. From the starting building, a player wants to eventually step on every building at least once. Movement is only allowed between neighboring buildings.

We are given a collection of small binary grids, each of size $m times m$, where each cell is either empty or filled.

We are given two arrays of equal length. The starting array can be modified step by step until it matches a target array.

We are asked to construct two bitstrings, call them s and t, with the same length and the same number of zeros and ones. Both strings are then transformed by repeatedly applying a substitution rule many times, specifically 22 times.

We are given a grid where every cell at coordinate $(i, j)$ has a value equal to $i times j$. A token starts at $(a, b)$ and must reach $(n, m)$.

We are simulating a two-candidate election system with a twist: each participant has a probabilistic vote, and we are allowed to “spend” a small number of boosts to increase some voters’ probabilities in discrete steps.

We are given a sequence of test results where each element represents a person’s COVID test outcome or a related status encoded as a simple value.

We are asked to count ways to split a total of N kicks into consecutive training sets. Each training set has a positive number of kicks, and these sizes form a sequence whose sum is exactly N. Two rules constrain this sequence.

We are dealing with a two-phase communication game built around a tree. In the first phase, Alice sees a rooted tree with nodes labeled from 1 to n. She is allowed to perform a small number of operations on a screen that starts as a length-n array filled with zeros.

The input describes a directed structure over numbered vertices where each vertex points to a “nearest” vertex.

The statement you provided for “Codeforces 106467G - CS:Go Over” is effectively empty, so there isn’t enough information to reconstruct what the problem is asking, what the input format looks like, or what the required output should represent.

We are given a rooted tree with $N$ vertices. Each vertex $i$ is assigned an integer, and all integers are constrained to lie in the range $[0, K]$. The assignment is not arbitrary: it must respect a structural counting rule that is defined recursively over subtrees.

We are given a tree where every vertex carries a distinct label from the set $0,1,dots,n-1$. Because the labels form a permutation, each value corresponds to exactly one node, so thinking in terms of values or nodes is interchangeable.

We are given a collection of rows, and for each row there are parameters that define how its contribution to the final answer depends on two global continuous variables. You can think of choosing a point in a 2D plane, and every row assigns a cost to that point.

We are given a directed graph with weighted edges, where each node represents a position on a board and each edge represents a move that increases or decreases a running score. Starting from node 1, we repeatedly choose any outgoing edge or stay in place with zero gain.