brain

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.

I can write the full editorial, but the problem statement for Codeforces 103993I - Lanterns is missing from your prompt. Right now I don’t know: - what the lanterns represent, - what the input describes, - what operation or optimization is required, - what needs to be computed.

I don’t have the actual problem statement for Codeforces 103993H - Report Preparation, so I can’t produce a correct editorial yet. Right now the prompt only contains the template, but no description of what the input represents, what needs to be computed, or any constraints.

I don’t have the actual problem statement for Codeforces 103993E - d-Sort, so I can’t reliably derive the algorithm, constraints, or edge cases needed for a correct editorial.

I’m missing the actual problem statement for Codeforces 103993F - Save the Magazines, so I can’t reliably reconstruct the model or write a correct editorial.

We are dealing with 6-digit passwords, where each password is a sequence of digits from 0 to 9. The structure of the password is highly constrained: it must use exactly two distinct digits, and each of those digits must appear exactly three times, so the password is always a…

I’m missing the actual problem statement for Codeforces 103993C - Reverse and Remove, so I can’t reliably reconstruct the intended solution or write a correct editorial.

The level is modeled as an infinite number line. A character starts at position 0 and wants to reach position n. At each moment, the character can either move one unit left or right, paying a fixed cost a seconds per unit step, or perform a teleport-like jump that moves…

The problem statement for Codeforces 103993B - Permutation Value is missing from your prompt, so there isn’t enough information to construct a correct editorial.

We are given a system consisting of several identical “machines” arranged in a fixed line. Each machine transforms a single integer value as it passes through. The transformation rules differ per machine, and they may either increase or decrease the current value.

The problem statement is missing from your prompt (both the description and input/output sections are empty), so there isn’t enough information to reconstruct what Codeforces 103994K “Не сортируй” is asking.

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

Let (55) denote the recursive apply procedure for $\mathrm{AND}(f,g)$ on BDDs, where each call is indexed by a pair of nodes $(u,v)$ and recursively generates calls on $(u_0,v_0)$, $(u_0,v_1)$, $(u_1,...

The problem statement for Codeforces 103994I - Make Nonzero Sum (hard) is missing from your prompt, so I don’t have the actual rules, inputs, or required output to base an editorial on.

I don’t have the actual problem statement for Codeforces 103994G - Split sort in your prompt, and the sections that matter (especially constraints and operations) are empty. Without that, I’d be forced to guess the task, which would make the editorial unreliable.

I can’t write a correct editorial for this one yet because the actual problem statement is missing. Right now I only see the template (input/output sections are empty), so there’s no way to reconstruct what “Башенки” is asking, what the constraints are, or what…

There is a mismatch in the prompt: Codeforces 103994F - Minecraft Series has no accessible public statement in the standard problemset, and the identifier does not correspond to a retrievable contest problem in the usual index.

I cannot reliably reconstruct Codeforces 103994E - “Самостоятельные деревья” from the sources available here, and guessing would very likely produce a completely wrong editorial.

I can’t write a correct editorial yet because the actual problem statement is missing. Right now only the title “Factorial Divisibility” is present, but there is no description of what is given, what must be computed, or the constraints.

I can’t reliably write a correct editorial for this without the actual problem statement. “Codeforces 103994C - The Beach” isn’t enough by itself, and I don’t have the input/output definition, constraints, or what needs to be computed.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only know the title “Фальшивая стопка” (which translates roughly to “Fake Stack”), but I don’t have the rules of the problem, the input format…

The problem statement is missing from your prompt (both the input/output sections are empty), so there’s no way to reconstruct what Codeforces 103994B is asking for.

I can’t write a correct editorial for “Codeforces 103997A - SuperMemo” without the actual problem statement.

Each query gives a contiguous segment of the array. Inside that segment, we consider all possible subsets. For each subset, we sort it in descending order and assign alternating signs starting with plus.

The problem statement is missing from your message, so I don’t have enough information to write a correct editorial.

I can write the full editorial in the exact style you want, but I’m missing the only thing that makes it possible: the actual problem statement.

I don’t have the statement for Codeforces 103999K - Iuli available in your prompt, and I can’t reconstruct it reliably from the title alone.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103999J - P-ON is missing from your prompt.

I don’t have the actual problem statement for Codeforces 103999H - for-for-for-for, so I can’t reliably derive the solution, constraints, or even the intended algorithm.

Let (55) denote the recursive apply procedure for $\mathrm{AND}(f,g)$ on BDDs, where each call is indexed by a pair of nodes $(u,v)$ and recursively generates calls on $(u_0,v_0)$, $(u_0,v_1)$, $(u_1,...

Let the vertex set be $V={1,\dots,12}$ and let $m=\binom{12}{2}=66$ be the number of possible edges.

Let the vertex set be $V={1,\dots,12}$ and let $m=\binom{12}{2}=66$ be the number of possible edges.

Let the vertex set be $V={1,\dots,12}$ and let $m=\binom{12}{2}=66$ be the number of possible edges.

The problem statement is missing from your prompt, so I don’t have enough information to write a correct editorial. Right now I only know the title “Dacians vs Samurai”, but there are no details about the input format, the operations, or what needs to be computed.

I can’t write a correct editorial yet because the actual problem statement for “Codeforces 103999G - Battle of Scundu” is missing.

Let the vertex set be $V={1,\dots,12}$ and let $m=\binom{12}{2}=66$ be the number of possible edges.

I don’t have the actual statement of Codeforces 103999F - Basketball, and without it I can’t reconstruct the problem or derive a correct solution.

The problem statement is missing from your prompt, so I can’t reliably reconstruct the task or write a correct Codeforces-style editorial.

We are given two strings, a longer text string and a shorter pattern string. The task is to determine how many times the pattern appears inside the text as a contiguous substring.

The problem statement section is empty, so there is no information about what “103999C - Prime” is actually asking.

The problem statement for Codeforces 103999D - Gioconda is missing from your message, so I don’t have the actual task description to base an editorial on. Right now I only see empty sections for Input/Output, which isn’t enough to reconstruct the problem reliably.

I can’t produce a correct editorial yet because the actual problem statement for Codeforces 103999B - Nitoiu is missing, and it does not appear to be accessible from the standard problemset content in the way typical Codeforces tasks are.

The problem statement section is empty, so there isn’t enough information to reconstruct what “William and Array” is asking.

The problem statement for Codeforces 104002H - William and will.i.am is missing from your prompt, so I don’t have the actual task description, input/output format, or constraints needed to write a correct editorial.

I can’t reliably write a correct Codeforces editorial for 104002D - William and Cornmeal from what you provided, because the actual problem statement is missing.

I can’t write a correct editorial for “Codeforces 104002G - William and Spaceport” because the problem statement is missing from your prompt.

I can’t reliably write a correct editorial here because the actual statement of Codeforces 104002F - William and Cards is missing from your prompt.

We are given a line of integers, and two players take turns removing elements until nothing remains. William moves first, and on his turn he can pick any still-available element from anywhere in the array.

We are given a line of workers, each worker having two attributes: productivity and working hours. The contribution of a worker is defined as the product of these two values.

The problem statement section in your prompt is empty, so there isn’t enough information to derive the task, constraints, or required algorithm. Without that, any editorial would be guessing, which defeats the purpose of a Codeforces-style writeup.

I’m missing the actual problem statement for Codeforces 104002A - William and Mary, so I can’t reliably reconstruct the task or write a correct editorial.

The problem statement is missing from your message (the sections for input/output and the actual description are blank), so there isn’t enough information to write a correct editorial.

I don’t have the actual problem statement for Codeforces 104003K - William and Necklace in your prompt, and I shouldn’t guess it because the editorial would end up fabricated.

The problem statement is missing from your prompt (the sections for Problem Statement / Input / Output are empty).

I can’t write a correct editorial yet because the problem statement for “Codeforces 104003H - William and will.i.am” is missing from your prompt.

The graph $P8 times P8$ is the standard $8 times 8$ rectangular grid graph. Each vertex corresponds to a cell $(i,j)$ with $1 le i,j le 8$, and edges connect horizontally and vertically adjacent cells.

I can’t reliably write a correct editorial for this yet because the actual problem statement (what operations are allowed, what input/output mean, constraints, etc.) is missing from the prompt.

We are given a row of cards, each card having a positive integer value. We are allowed to perform a local transfer operation between adjacent positions: if we look at positions i-1 and i, and the value at i is even, we may move one factor of 2 from card i to card i-1 by…

Let $V={1,2,\dots,12}$ and let each simple undirected graph on $V$ be identified with a binary vector over the $\binom{12}{2}=66$ edges, so the total set of graphs is ${0,1}^{66}$.

William repeatedly serves dessert to groups of friends arriving over time. The key constraint is that at every moment, after a new group arrives, the dessert must be cut into some number of equal slices so that every currently present person can be given an integer number of…

The problem statement is missing from your prompt (both “Problem Statement”, “Input”, and “Output” sections are empty), so there’s no way to reconstruct what Codeforces 104003C - William and Middle Management is actually asking.

The graph $P8 times P8$ is the standard $8 times 8$ rectangular grid graph. Each vertex corresponds to a cell $(i,j)$ with $1 le i,j le 8$, and edges connect horizontally and vertically adjacent cells.

We are given a permutation of size $n$, and we repeatedly apply two operations to it. After each operation, we are asked to compute how many swaps Bubble Sort would perform if it were run from scratch on the current permutation.

We are asked to split a single wooden bar of total integer length $m$ into exactly $n$ positive integer pieces. After cutting, we look at two quantities of the resulting multiset of lengths. The first quantity is the “capacity”, defined as the smallest piece length.

We are given a partially filled permutation of size $n$. Some positions already contain fixed values from 1 to $n$, and the remaining positions are empty and must be assigned the unused numbers so that the final array becomes a valid permutation.

Let the vertices of $P8 times P8$ be the lattice points $$V = {(i,j) mid 1 le i,j le 8},$$ with edges between vertices that differ by $1$ in exactly one coordinate.

We are given a circular track made of $n$ cells. Each cell has a difficulty value $di$. A race starts at a chosen cell $s$, and a fixed amount of time $t$ is allowed. The racer moves forward cell by cell in circular order.

We are given a collection of distinct lowercase strings. Each string can be thought of as a label. We are interested in nested substring relationships between triples of different strings.

Each trial in this process produces either a “special” doll or a “normal” one. A special doll appears with probability $p = frac{a}{b}$, and Cirno repeats independent trials until she has collected exactly $n$ special dolls.

We are given several geometric regions in the plane. Each region is a circular sector: a portion of a disk defined by a center point, a radius (implicitly given by distance from the center to two boundary points), and an angular span between two rays starting at the center.

Let the vertices of $P8 times P8$ be the lattice points $$V = {(i,j) mid 1 le i,j le 8},$$ with edges between vertices that differ by $1$ in exactly one coordinate.