brain

We are given a collection of problems, each characterized by a single integer value that represents how many trailing zeros its difficulty scale has in a power of ten.

The task is intentionally minimal. There is no input to process, no computation to perform, and no decision to make. The program is expected to produce a single fixed string on standard output.

We are given a sequence of elves arriving one by one. Each elf has a sickness threshold $si$. We also have a fixed set of dishes, each with a health value $h$ and a tastiness value $t$.

We are given two trees built on the same set of labeled leaves. Internal structure can differ between the two trees, but the leaves represent the same entities in both. The task is to compare how triples of leaves behave in the two trees.

The core object in this problem is a self-describing integer sequence, the Golomb sequence. Each value describes how many times integers appear later, and at the same time those repetitions define the next values, which creates a recursive structure where the sequence encodes…

We are given a collection of integers that represent positions on a circular “password lock”, together with a modulus value $k$.

We are given a sequence of integers, where each integer is written in decimal form and may contain leading zeros. For every number, we are allowed to freely reorder its digits before using it.

We are given a sequence of elves arriving one by one. Each elf has a sickness threshold $si$. We also have a fixed set of dishes, each with a health value $h$ and a tastiness value $t$.

The input describes a tree of chambers, where each chamber initially contains some amount of cheese. A mouse starts at chamber 1 and tries to reach chamber n, which is the exit. The mouse moves in discrete steps.

The editorial can’t be written yet because the actual problem content is missing. Right now there is no description of what “Codeforces 104114N - Nusret Gökçe” is asking for, and the Input/Output sections are empty.

The game consists of a sequence of realms that must be cleared in order. The player starts in realm 1 with level 1 and some initial health that we are free to choose.

We are working with a weighted undirected graph where the vertices are numbered from 1 to n. Each edge connects two vertices and has a positive cost. A key structural restriction is that every edge only connects vertices whose labels differ by at most 10.

We are given a stack-based puzzle involving three rods and a collection of disks with distinct sizes from 1 to n.

We are given a sequence of nonnegative integers arranged in a line. Each operation picks two adjacent positions and replaces both values with the same number, specifically the maximum of the two values minus one, as long as that maximum is positive.

I can’t write a correct Codeforces 104120F editorial as requested because the problem statement is missing entirely (the “Problem Statement / Input / Output” sections are empty).

We are given a line of fixed axle positions, already sorted from left to right, and we must assign a given multiset of gear radii to these axles. Once placed, every neighboring pair of gears must be tangent.

We are given a complete weighted graph on $n$ players. The weight between player $i$ and player $j$ is a symmetric value $P{i,j}$, which represents the popularity gain if those two players play a match. A match always eliminates one player.

We are given a collection of 2n students, each with a numeric skill value. Initially, they are grouped into fixed pairs, specifically consecutive indices, so student 1 is paired with 2, student 3 with 4, and so on.

We are given a set of people and a collection of group COVID tests. Each test checks a subset of people and returns positive if at least one infected person is inside that subset.

We are given a unit square cake that contains two types of points: chocolate chips and strawberries. We are allowed to draw exactly one straight line segment that cuts through the cake.

We are given a base string s. Each day, Momo does not modify it internally, but instead builds a longer string by concatenating copies of the original s. After day 1, the string is exactly s. After day 2, it becomes s + s. After day k, it becomes s repeated k times in a row.

We are dealing with sequences formed from bracket-like operations where we build a structure step by step and are asked to compute the probability that the resulting sequence satisfies correctness conditions of a bracket system.

We are given an $n times n$ grid where each cell must be assigned a letter from 'a' to 'z', and these letters define a priority ordering, with 'a' being the highest priority and 'z' the lowest. A robot starts at cell $(1,1)$.

We are given a string consisting of lowercase English letters and asked whether it can be split into exactly k contiguous non-empty pieces such that every piece contains the same number of consonant letters. A consonant here means any letter except a, e, i, o, u, y.

We are given a quadratic equation with integer coefficients $a, b, c$, all of them nonzero. We are allowed to replace any subset of these three coefficients with new nonzero integers.

We are given a partially observed state of a standard 52-card deck and a hand of cards already taken by a player.

We are maintaining an array of non-negative integers under two types of operations. The first operation applies a bitwise XOR with a given value to every element in a contiguous subarray.

There is a row of $n$ chests numbered from 1 to $n$. Exactly one chest $k$ contains treasure, while all others are empty. A pirate starts opening chests but has not yet discovered where the treasure is located.

We are given two geometric pieces, each described as a quadrilateral with a very specific structure: a right trapezoid.

We are given a set of time intervals representing TV programs. Each program has a start time, an end time, and one of three types. Type 1 programs are preferred by Petya, type 2 by Masha, and type 3 by both of them simultaneously.

We start with an infinite sequence of natural numbers written in order, essentially 1, 2, 3, 4, 5 and so on. We are interested in how this sequence changes after a series of deletion operations. Each operation is defined by a step value y.

We are given a deterministic sequence generated by a linear recurrence under a modulus. Starting from an initial value s, every next value is produced by multiplying the previous value by a, adding b, and then reducing modulo a large prime p.

We are given a simplified description of a keyboard where each key corresponds to an uppercase letter arranged in three rows. Some of these keys are marked with an asterisk, meaning they are “oily”, and every other key is clean.

We are given a large set of items arranged in a strict dependency system. Some items are basic resources that already exist in limited quantities, while all other items are produced by recipes that consume previously defined items.

We are given a rectangular grid where each cell is either land or water. Exactly three cells are already land, and we are allowed to convert any number of water cells into land.

We are given a sequence of exercises. For each exercise, Bob has three possible choices: skip it, do an easy version, or do an intense version. Each choice has an energy cost of 0, $ai$, or $bi$ respectively, with $ai < bi$.

We start with a complete undirected graph on $n$ vertices, where vertex labels represent a strict ordering of “power”. Every pair of vertices is initially connected by a single edge.

We are given a fixed step size $k$. We are also given $n$ time intervals, each interval representing a range of days during which a particular item is being sold. The merchant appears periodically depending on our choice of a starting day $s$.

We are given a line of n factions, each sitting in a fixed west-to-east order and each carrying a wealth value. Over time, factions disappear one by one until only a single faction remains.

We are given a weighted graph where cities are nodes and roads are undirected edges, each taking exactly one hour to traverse. From a starting city, we want the minimum time to reach a destination city. The complication is that there are patrol cars moving on fixed cyclic routes.

Let $f(x_1,\dots,x_n)$ be a Boolean function, and let $G(z)$ be its generating function in the sense of Exercise 25, so that G(z)=\sum_{x\in\{0,1\}^n} f(x)\, z^{w(x)}, where $w(x)=x_1+\cdots+x_n$ is t...

We are given the first $n$ prime numbers and we must split them into two groups: one for Alice and one for Bob. Each prime is indivisible and must go entirely to exactly one of them.

We are given an array of integers representing values written on students’ shirts. Each day, every position updates its value simultaneously based on a global statistic: a value v becomes the number of occurrences of v in the entire array on that day.

We are given a function $f(x)$ defined on real numbers, but split into three regions of $x$. Each region uses a different formula: a linear expression on the far left, another linear expression in the middle, and a cubic polynomial on the right.

I can’t reliably write a correct editorial for this yet because the actual problem statement for Codeforces 1041193 - “Престижный номер” is missing from your prompt.

I can’t write a correct editorial for this problem yet because the statement is missing (the input/output description and constraints are required to derive any solution structure).

I’m missing the actual problem statement for Codeforces 1041194 - “Морской бой”, so I can’t reliably reconstruct the rules or the required computation.

The problem statement section is empty, so there’s no way to reconstruct what “Майки и носки” is actually asking for. For Codeforces editorials, the solution, invariants, and even the complexity depend entirely on the task definition.

I can’t write a correct editorial yet because the actual problem statement is missing. Right now I only know the title “Самолёт (Airplane)”, but there is no description of: - what the input represents, - what is being computed, - constraints, - or samples.

Let $f(x_1,\dots,x_n)$ be a Boolean function, and let $G(z)$ be its generating function in the sense of Exercise 25, so that G(z)=\sum_{x\in\{0,1\}^n} f(x)\, z^{w(x)}, where $w(x)=x_1+\cdots+x_n$ is t...

The problem statement for “Codeforces 104120K - Keypad Repetitions” is missing from your prompt, so I don’t have enough information to write a correct editorial.

The problem statement section is empty, so there isn’t enough information to write a correct editorial. For a Codeforces editorial, I need at least the full description of what “Ladybug And The Bullet Train” is asking: the input format, what is being simulated or computed…

We are given a tree with n cities connected by n − 1 undirected roads. Every road must be assigned a direction, turning the undirected tree into a directed structure where each edge becomes a one-way connection.

I don’t have the actual statement for Codeforces 104120I - Ivan And Mega Queries in your message, so I can’t reliably reconstruct the problem or produce a correct editorial without guessing.

I can’t write a correct Codeforces 104120F editorial as requested because the problem statement is missing entirely (the “Problem Statement / Input / Output” sections are empty).

The problem statement is missing from your prompt, so I don’t have enough information to write a correct editorial for Codeforces 104120G - Hola.

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 104120H - Homework is missing from your prompt.

I can write the full Codeforces-style editorial, but I’m missing the actual problem content for 104120E - Exam Period (statement, input, output, constraints).

The problem content is missing from the prompt. Right now, only the title “Codeforces 104120D - Denji1” is provided, but the actual statement, constraints, input/output format, and samples are empty.

Connection interrupted. Waiting for the complete answer

I can write the full editorial in exactly that style, but I’m missing the actual problem statement for Codeforces 104120B - Business Stamps.

The prompt is missing the actual problem statement for “Codeforces 104120C - Company Layoffs”, so there isn’t enough information to reconstruct the model, constraints, or intended solution.

Let $h{a,b}(x)=((ax+b)gg(n-l)) bmod 2^l$, with $ain A={amid 0<a<2^n, a text{odd}}$ and $bin B={bmid 0le b<2^{n-l}}$. For fixed sets $P$ and $Q$ of $n$-bit integers, define $$I={h{a,b}(p)mid pin P},qquad J={h{a,b}(q)mid qin Q}.$$ Let $ $$Pr[h{a,b}(x)=h{a,b}(y)]le 2^{-l}.

Exercise 31 provides a method for evaluating a BDD by interpreting each sink and branch node as an element of an algebraic system equipped with operations $\circ$ and $\bullet$, and propagating values...

The problem statement is missing from your message, so there’s no way to reliably reconstruct the model, constraints, or required algorithm.

I can’t reliably write a correct editorial for “Codeforces 104128L - Proposition Composition” without the actual problem statement.

I can write the full editorial in the exact style you requested, but I’m missing the only thing needed to make it correct: the actual problem statement for Codeforces 104128J - Perfect Matching.

I can’t write a correct editorial for “Codeforces 104128I - Perfect Palindrome” as-is because the actual problem statement is missing from your prompt. Right now I don’t know: - what the input structure is (string, array, multiple test cases, etc.

Let $h{a,b}(x)=((ax+b)gg(n-l)) bmod 2^l$, with $ain A={amid 0<a<2^n, a text{odd}}$ and $bin B={bmid 0le b<2^{n-l}}$. For fixed sets $P$ and $Q$ of $n$-bit integers, define $$I={h{a,b}(p)mid pin P},qquad J={h{a,b}(q)mid qin Q}.$$ Let $ $$Pr[h{a,b}(x)=h{a,b}(y)]le 2^{-l}.

I can’t write a correct editorial for “Codeforces 104128H - Factories Once More” because the problem statement is missing from your prompt. Right now there’s no information about: - what the “factories” are in the model (graph, array, tree, etc.

I can’t reliably write a correct editorial for Codeforces 104128G - Inscryption from just the title. The full solution depends entirely on the actual rules (game mechanics, operations allowed, constraints, and what is being optimized or decided).

The problem statement for “Codeforces 104128F - Triangles” is not included in your message, so I don’t have the actual definitions of the input, output, or the task the solution is supposed to solve.

I can’t reliably write a correct editorial for this without the actual problem statement. “Codeforces 104128E - Color the Tree” isn’t identifiable from the title alone, and guessing would very likely produce the wrong model, wrong constraints, and therefore a misleading…

Let $G$ be the given FBDD with node set $V(G)$.

I can’t write a correct editorial yet because the actual problem statement for “Codeforces 104128D - Chat Program” is missing from your prompt.

I can’t reliably write a correct Codeforces editorial for “104128C - Fabulous Fungus Frenzy” because the actual problem statement, input format, and constraints are missing from your prompt.

I’m missing the actual problem statement for Codeforces 104128B - Ropeway, and without it I can’t produce a correct editorial.

The statement for Codeforces 104135I (“НОД и подмножества”) is not included in your message, so I don’t have enough information to reconstruct the task reliably.

I can’t write a correct editorial for this yet because the actual problem statement is missing from your prompt. Right now I only see the title “Сложная матрица” and no description of what the matrix operations or required output are.

Let $h{a,b}(x)=((ax+b)gg(n-l)) bmod 2^l$, with $ain A={amid 0<a<2^n, a text{odd}}$ and $bin B={bmid 0le b<2^{n-l}}$. For fixed sets $P$ and $Q$ of $n$-bit integers, define $$I={h{a,b}(p)mid pin P},qquad J={h{a,b}(q)mid qin Q}.$$ Let $ $$Pr[h{a,b}(x)=h{a,b}(y)]le 2^{-l}.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Codeforces 104135G - Задача о перестановках”, but no description of what is given, what needs to be computed, or the…

I can’t write a correct editorial yet because the actual statement of Codeforces 104135F - “Крош и интересные пары чисел” is not included in your prompt, and it is not available in a clean form from the metadata we currently have.

Let $B$ be the BDD of $f(x_1,\dots,x_n)$ with root node $r$.

The problem statement section is empty, so there is no way to reconstruct what “Крош и строка” is actually asking. Any attempt to write a full editorial without the task definition would be guesswork and would likely produce a completely incorrect solution.

We are given a sequence of numbers representing a row of elements, each element having two attributes: a value and a removal cost. The game allows us to repeatedly pick two adjacent elements and delete the smaller-valued one, paying its associated removal cost.

I can’t reliably write a correct editorial for Codeforces 104135D - “Дождь” without the actual problem statement. Right now I only have the title, but no description of what the input/output represents or what the task is asking.

The problem statement for Codeforces 104135A - “Крош и пароль” is missing from your prompt, so there’s no reliable way to reconstruct the solution or write a correct editorial without guessing.

We are given an undirected graph where each vertex is a named place inside a university building. Some of these places are special: the starting point is deansoffice, the destination is street, and there is exactly one additional mandatory place, the room where the student’s…

Let the BDD represent $f(x_1,\dots,x_n)$ with variable order $x_1 < x_2 < \cdots < x_n$.

I can’t reliably reconstruct Codeforces 104142J (“Плоские фигуры”) from the title alone, and writing a correct editorial without the actual statement would risk inventing constraints, rules, or even the task itself.

The problem statement is missing from your prompt, so there is no way to reconstruct the task, constraints, or intended solution for “Codeforces 104142I - WA 132”. An editorial depends entirely on knowing what the input represents and what needs to be computed.

I can’t write a correct editorial for this without the actual problem statement. Right now the only thing available is the title, but “Сбалансированные деревья” (Balanced Trees) could correspond to multiple different tasks, and the required data…

The problem statement is missing from your prompt (both the input and output sections are empty), so there isn’t enough information to write a correct Codeforces editorial.

I can’t write a correct editorial for this problem yet because the actual problem statement is missing from your message. “Codeforces 104142E - Квадраты” alone isn’t enough to reconstruct the task reliably.

I can’t write a correct Codeforces editorial for this problem yet because the actual problem statement is missing. Right now I only have the title “104142F - Забор”, but no description of what the input represents, what needs to be computed, or even the constraints.

The statement content is missing in the prompt, so there isn’t enough information to reconstruct Codeforces 104142D (Пляж) reliably.

I can write the full editorial in exactly that format, but I’m missing the actual problem statement for Codeforces 104142B - Шифр.

This problem strips away all structure and asks for a fixed output regardless of the input. You are given some input stream, which may contain anything, but none of it influences the required result. The task is simply to produce a single exact string as the program’s output.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 104142C - Окружности” is a geometry problem (circles), but without the exact rules, input format, and required output, any solution would be guesswork.

Exercise 31 describes a generic BDD evaluation scheme in which a function is computed by replacing each internal decision node labeled by variable $x_j$ with an algebraic combination of the values of...