brain

We are given a sequence of integers. Think of them as daily “changes” to some running value that starts at zero. As we go from left to right, we maintain a running sum. Each element either increases or decreases this running sum.

Let Eq.

The problem statement is missing from your message, so I don’t have enough information to reconstruct the task or derive a correct solution.

We are given a sequence of positions arranged in a line, where each position carries a certain weight. Then we are given a collection of independent queries. Each query describes a process that starts from a given index and repeatedly jumps forward by a fixed step size.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now we only have the title “Халат Рика”, but no description of the rules, input format, or what needs to be computed.

I can’t write a correct editorial for CF 103966F without the actual problem statement. Right now the prompt only contains the title (“Артефакты”) but no description, input/output format, constraints, or samples.

The problem statement for “Codeforces 103966E - Инопланетные кальмары” is missing from your prompt, so there is no way to reconstruct the required algorithm, reasoning, or implementation correctly.

I’m missing the actual problem statement for Codeforces 103966A - “Стрельба из пушки”, so I can’t reliably reconstruct the task or derive the correct algorithm without risking inventing details.

I can’t reliably write a correct editorial for “Codeforces 103966C - Планеты двух измерений” because the actual problem statement is missing from your prompt.

The problem statement is missing from your prompt, so I don’t have the actual task details (input format, required output, or constraints). Without that, any “editorial” would be guesswork, and for Codeforces problems that quickly turns into something misleading.

We are given a string consisting of lowercase letters. We are allowed to choose an integer parameter $k$. Once $k$ is fixed, we repeatedly take every contiguous substring of length $k$, starting from left to right, and reverse each one in sequence.

The problem statement is not included in your prompt (both the Problem Statement, Input, and Output sections are empty). Without that, it’s impossible to write a correct editorial, since the solution structure, constraints, and even the task type are unknown.

I don’t have the actual statement of Codeforces 103967G (“Незваные гости”) in your prompt, so I can’t reconstruct the problem, constraints, or the intended solution reliably.

The problem statement is missing from your prompt (both the description, input/output, and constraints are empty), so I don’t have the actual task definition for Codeforces 103967I.

I cannot find a reliable public statement or mirrored statement for Codeforces 103967F - “Артефакты”, and it does not appear in the standard Codeforces problemset archives or contest listings accessible from typical indices.

I don’t have the actual statement of Codeforces 103967B - “Иерархия цитадели” in your message, so I can’t reliably reconstruct the problem or produce a correct editorial.

The problem statement is missing from your message, so I can’t reconstruct a correct editorial for “103967E - Эффективный двигатель” without risking inventing details that may be wrong.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only have the title “Symmetric cards”, but nothing about what the cards contain, what symmetry means in this context, or what transformations or queries are involved.

I’m missing the actual problem statement for Codeforces 103967C - “Защитное поле”, so I can’t reliably reconstruct the solution or write a correct editorial.

The problem statement section is empty, so there is no way to reconstruct what “103967A - Стрельба из пушки” is actually asking for.

I don’t have the actual statement for Codeforces 103968H - Janky Jaffa Cakes, so I can’t derive a correct solution, constraints analysis, or examples without risking hallucinating the problem.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Gingerbread House Decorations”, but there is no description of the rules, inputs, or required output.

The problem statement is missing from the prompt, so there is no way to reliably reconstruct the task, constraints, or required algorithm for Codeforces 103968E - Brownie Brawl. Right now we only know the title, which is not enough to derive a correct solution.

I don’t have the actual statement for Codeforces 103968F - Seeking Starburst in your prompt, so I can’t reliably reconstruct the problem or produce a correct editorial without guessing.

Let $f$ be a Boolean function of variables $x_1, x_2$, taking values in ${\bot,\top}$, with the usual ordering $\bot < \top$.

I can write the full editorial, but I’m missing the actual problem statement for “Codeforces 103968C - Wedding Cake”.

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 103968D - Splitting Jellybeans is missing from your prompt. Right now I don’t know: - what the jellybeans represent (array? multiset? tree? values?

Let $Q8$ be the queen graph on the $8times 8$ chessboard. Its vertex set $V$ has $ All families are represented in the sense of Section 7.1.

The problem statement is missing from your prompt, so I can’t reconstruct what Codeforces 103968B - Sour Skittles is actually asking. Right now I only know the title, but not the rules, input format, or required output.

The problem statement for Codeforces 103969J - Pudding Passes is missing from your message, so I don’t have enough information to write a correct editorial. Right now I only know the title, but not the rules of the process, the input format, or what needs to be computed.

The problem statement for Codeforces 103969I - Ice Cream Orders is missing from your message, so I don’t have the actual rules, inputs, or required computations needed to write a correct editorial.

Let $G=(V,E)$ be a finite graph. A set $Dsubseteq V$ is dominating when every vertex $vin Vsetminus D$ has a neighbor in $D$. A kernel $Ksubseteq V$ is an independent set such that every vertex $vin Vsetminus K$ has a neighbor in $K$. Let $K$ be a kernel of $G$.

The problem statement for “Codeforces 103969H - Janky Jaffa Cakes” is not included in your prompt, so there is no way to reconstruct the actual task, constraints, or required algorithm.

I can’t reliably write a correct editorial for this yet because the actual problem statement is missing from your prompt. Right now I only see the title “Seeking Starburst”, but no description of what the input/output mean, constraints, or what is being optimized.

The problem statement is missing from the prompt, so there isn’t enough information to write a correct or meaningful editorial. Right now I don’t know what the input represents, what operations are allowed, or what needs to be computed.

We are given a sequence of days, and on each day Mel receives a single cake layer ingredient labeled from 1 to 5. Mel is building wedding cakes, and each complete cake must be assembled in strict order from layer 1 up to layer 5.

I can’t write a correct editorial yet because the actual problem content for Codeforces 103969E - Brownie Brawl is missing from your prompt.

Let $G=(V,E)$ be a finite graph. A set $Dsubseteq V$ is dominating when every vertex $vin Vsetminus D$ has a neighbor in $D$. A kernel $Ksubseteq V$ is an independent set such that every vertex $vin Vsetminus K$ has a neighbor in $K$. Let $K$ be a kernel of $G$.

We are given a graph that is already guaranteed to be bipartite. This means the vertices can be split into two groups such that every edge connects vertices from different groups. On top of this structure, some vertices are already assigned colors: red, blue, or uncolored.

We are given many independent values of $n$. For each $n$, we must construct two integers $x$ and $y$ such that $y - x = n$, while also ensuring that $x$ and $y$ have the same number of prime factors when counted with multiplicity.

Let variables be ordered $x_1 < x_2 < \cdots < x_n$.

We are given a grid made of n × m cells. Each cell is either empty or marked as red. Our task is to decide whether the red cells form exactly one of four predefined geometric patterns named H, U, S, or T.

We are given two kings on an infinite chessboard. One king belongs to Walk Alone (white) and the other to Salix Leaf (black). They alternate moves starting with white, and each king moves like a standard chess king, meaning it can step to any of the eight neighboring squares.

Let $G=(V,E)$ be a graph. A set $Ksubseteq V$ is a kernel of $G$ when it is independent and every vertex $vin Vsetminus K$ has a neighbor in $K$. A set $Dsubseteq V$ is a dominating set when every vertex $vin Vsetminus D$ has a neighbor in $D$.

We are given a tree of buildings. Each building is a node and each road is an edge, and the structure guarantees there is exactly one simple path between any two nodes. Two people start simultaneously: one starts at node $a$, the other starts at node $b$.

We are given two strings, a source string s and a target string t. From s, we want to pick a contiguous segment, and we want this segment to match a prefix of t after we are allowed to modify t in a very specific way: we may choose a length k and reverse the first k characters…

We are given a rooted tree of formulas. Each node represents a formula, and each formula has an energy cost that is paid when Walk Alone has to “learn” it again.

We are given several piles of stones, each pile having a positive integer size. We repeatedly merge two existing piles until only one pile remains.

We are given a bitwise transformation applied to a fixed number of bits. An unsigned integer x is represented using exactly k bits, so every value lies in the range from 0 to 2^k - 1. We are also given an array of operations.

We are given a set of consecutive integers starting from 1 up to a large upper bound of the form $nm + k$. From this set, we consider all possible subsets. For each subset, we compute the sum of its elements, then reduce that sum modulo $m$.

We are simulating a sequential combat game where a player fights monsters one after another in a fixed order. Each monster has a fixed attack threshold, and the player maintains a single integer state representing their current attack ability.

We are given two circles with radii $a$ and $b$. One circle is fixed in place, and the other circle is placed tangent to it from the outside.

I can’t write a correct editorial for this yet because the problem statement for Codeforces 103984J - Split and Sum is missing from your prompt.

I can write the full editorial, but I’m missing the only thing that makes it possible: the actual problem statement for Codeforces 103984I - “ТВ”.

The problem statement is missing from your prompt, so I don’t have the actual task definition (only the title “Тимбилдинг”).

I’m missing the actual problem statement for Codeforces 103984E - Division, so I can’t safely reconstruct the solution or write a correct editorial without risking inventing the wrong task.

I can’t reliably write a correct editorial for this without the actual problem statement. “Codeforces 103984G - Прямоугольная ломаная” only gives the title, but the solution, invariants, and even the data structures depend entirely on what is being…

I can’t write a correct editorial for this problem yet because the actual problem statement is missing from your prompt.

The problem statement is missing from your prompt, so there isn’t enough information to reconstruct the solution or write a correct editorial.

I’m missing the actual problem content for “Codeforces 103984D - Сборы в поход”. The statement, input/output description, and constraints are not included, so there’s nothing concrete to base an editorial on.

I can’t write a correct editorial yet because the problem content for Codeforces 103984B - “Фэйк Ньюз” isn’t included in your message (the statement, input/output, and constraints are missing).

I can’t produce a correct editorial yet because the problem statement for Codeforces 103984C - “Отборочный этап” is not included in your prompt, and it is not uniquely recoverable from the contest ID alone.

We are given a list of non-negative integers, each representing a value assigned to a person in a group. The task is to compute a global measure of “group cohesion”, defined as the sum over all unordered pairs of people of the bitwise AND of their values.

We are given a sequence of delivery points on a number line that must be visited in a fixed order. Two couriers start at known positions on the same line.

We are given a tree with $n$ vertices, where vertex 1 is the start and vertex $n$ is the destination. Each edge connects two vertices, but unlike a standard weighted tree, every edge is directed in a sense: if we traverse it from $u$ to $v$, we gain one value, and if we…

We are given a final visible sequence of candy wrappers arranged in the order the candies were eaten. Each wrapper is either red, blue, or unknown. The unknown symbol means we cannot see whether that eaten candy was red or blue.

We are given a sequence of mountain heights. For any choice of two distinct positions $l < r$, consider the segment of mountains between them, including both endpoints.

The median operator $\langle fgh\rangle$ is the Boolean function that is $1$ exactly when at least two of its arguments are $1$, and $0$ otherwise.

We are given a binary row of length $n$. Initially every position contains the same type of coin, which we can think of as “inactive”.

We are given a sequence of book titles, each title being a list of integers. Each integer represents a letter in a large alphabet. Every letter can appear in two forms: lowercase and uppercase.

We are given a set of distinct points on a plane representing stars. No three points lie on the same straight line, which removes degeneracies in geometric orientation checks.

We are given a rectangular painting of width $w$ and height $h$. Two identical square light sources are placed on the left and right vertical sides of this rectangle.

We are given a set of princes and a set of princesses. Each princess arrives with a fixed amount of dowry and two specific princes she is willing to marry. If she is used in the final arrangement, she must be matched to exactly one of those two princes.

We are given a fixed list of intervals on the number line. Each interval contributes its own length, and we will repeatedly select a segment of indices from this list.

We are given a static sequence a of length n. Each element a[i] is an integer and can be thought of as a label pointing into an infinite array S, which is indexed by all integers. Every position S[x] starts at zero and can be updated independently.

We are given a bipartite graph where the left side has $n$ nodes and the right side has $m$ nodes. Each node carries a value, and edges only connect left nodes to right nodes.

Each fan of AoShen secretly has an integer as their favorite value, but we are not given these values directly. Instead, every fan reports a number that represents how many distinct favorite values exist among all other fans except themselves.

We are given a permutation of length n, where each position contains a unique height from 1 to n. The goal is to transform this permutation into sorted order using a specific type of swap: we may pick two indices i < j such that the left value is larger than the right value…

We are given an array of integers representing the hunger levels of a line of chipmunks. A specific chipmunk indexed by k must always be included. We are allowed to choose any contiguous segment [l, r] such that it contains index k.

Let $G = (V,E)$ and let $g$ denote the family of edges encoded in the sense of Exercise 236(e), so that $g = bigcup{u-v in E}(eu sqcup ev)$ and the family of independent sets is expressed by a formula in the extended family algebra as in that exercise.

Let $x=(x_{15}\ldots x_0)_2$ and $y=(y_{15}\ldots y_0)_2$.

We are given several independent test cases. Each test case describes a collection of stone piles, and two players play an alternating game starting from Alice. On Alice’s turn, she chooses a single pile and removes any positive number of stones from it.

Each task gives a starting index $i$, and the required computation is always the same: sum three consecutive integers centered at $i$, specifically $(i-1) + i + (i+1)$. Algebraically this simplifies to $3i$, so every task is effectively asking us to compute a multiple of three.

The input is deliberately misleading. We are given an arbitrary string, but it carries no information relevant to the computation. The task is actually centered on a fixed mathematical expression: a definite integral over a full period from zero to two pi.

We are given a binary string representing a one-dimensional line of cells. Each cell holds either 0 or 1. We are asked to simulate exactly one step of a cellular automaton known as Rule 110.

Let $G = (V,E)$ and let $g$ denote the family of edges encoded in the sense of Exercise 236(e), so that $g = bigcup{u-v in E}(eu sqcup ev)$ and the family of independent sets is expressed by a formula in the extended family algebra as in that exercise.

We are given a circular menu of video streams. George starts with a cursor fixed on stream 1. He can repeatedly press three types of buttons a total of $m$ times: move the cursor one step left on the circle, move it one step right, or play the currently selected stream.

We are given a single very large nonnegative integer $N$ written in decimal. Conceptually, we want to rewrite this number in base 6, using digits from 0 to 5, with no leading zeros except for the number zero itself.

Let $U$ be the vertex set of the graph $G$ in (18), and let $g$ be its family of edges, encoded as in exercise 236(e), so each $e in g$ is a 2-element subset of $U$. A set of vertices $C subseteq U$ is a clique in $G$ if every pair of distinct vertices in $C$ is an edge of $G$.

We are given a large integer $k$, and we want to express the value $k^2$ as the sum of two special values. Each value comes from a fixed set indexed by integers $x$ in the range $1 le x le 2125$, and the value associated with index $x$ is $x^1$, which is just $x$ itself.

We are given six regional contests, each identified by a host country. Every region comes with five integers describing its participation structure: numbers from preliminary contests and regional contests, split by teams and universities, plus the number of foreign teams in…

We are given an array of values and a long sequence of updates. Each query either increases a whole segment by a constant, overwrites a segment with a constant value, or asks whether a given subarray has a special “balanced” property.

We are given a grid of lowercase letters. Think of it as a maze where every cell is a node, and you can move in four directions as long as you stay inside the grid.

Let $U$ be the vertex set of the graph $G$ in (18), and let $g$ be its family of edges, encoded as in exercise 236(e), so each $e in g$ is a 2-element subset of $U$. A set of vertices $C subseteq U$ is a clique in $G$ if every pair of distinct vertices in $C$ is an edge of $G$.

Let $x=(x_{15}\ldots x_0)_2$ and $y=(y_{15}\ldots y_0)_2$.

Let $G = (V,E)$ denote the contiguous-USA graph of (18), and let $U subseteq V$. The induced subgraph $G mid U$ is bipartite if and only if it contains no cycle of odd length, equivalently if and only if every connected component of $G mid U$ admits a 2-coloring.

I can’t write a correct editorial for “Antifibonacci Cut” without the actual problem statement. Right now the task only contains metadata, but none of the essential details like what the input represents, what “cut” means, what constraints are, or what defines an…

The problem statement for Codeforces 103993L - Intersection and Union is not included in your prompt, so there is no way to correctly reconstruct the intended task, constraints, or required output.

I can’t reliably write an editorial for Codeforces 103993K - FTL because the actual problem statement (inputs, outputs, constraints, and rules) isn’t included in your prompt.

The problem statement for “Codeforces 103993J - Problem with Random Tests” is not included in your prompt, so there is no way to reconstruct the algorithm, constraints, or even the required task from the information given.