brain

We are simulating a supermarket with several checkout queues. Customers arrive, choose a queue, and then stay in that queue until they are processed in order.

We are maintaining a dynamic array of glove sizes arranged in a line. At any moment, two things can happen. Either a single position changes its value, or we are given a query that focuses on a fixed subsegment of the array, and we must decide whether we can pick four distinct…

We are given a circle of positions, each holding some number of maracas. The only thing that matters about each position is whether its count is even or odd, because only even counts are acceptable in the final configuration.

We are given an undirected, connected graph with $N$ vertices and $M$ edges. Each vertex represents a tourist attraction, and edges represent streets that can be traveled in both directions.

We are given a system of $m$ symbols, each initially in one of two states, and a set of $n$ switches (levers). Each lever is connected to exactly two distinct symbols. Pulling a lever flips the state of both connected symbols: a 0 becomes 1 and a 1 becomes 0.

We are given a sequence of levels played in a fixed order. At the start, a hero has some initial power, and at each level there are two monsters available.

We are given a set of drones fixed in three-dimensional space. Each drone i has coordinates (xi, yi, zi) and a weight wi. We are free to choose the position of a special primary drone at any integer coordinate (x, y, z).

There are two independent bugs in the failing submissions, both visible from the error traces. First, the input is being parsed using input() or int(input()), assuming a clean token structure like: But the provided test input is heavily malformed from the program’s…

We are working in a $k$-dimensional grid space where a large axis-aligned hypercube $A$ spans from the origin to the point $(n, n, dots, n)$. Inside this big hypercube, we consider every possible smaller axis-aligned integer-coordinate hypercube $B$ that fits entirely inside $A$.

The brute-force method iterates over each suffix starting at index i, then tries every possible choice of three cut points i < a < b < c ≤ n. For each such split, it checks whether S[i:a] == S[a:b] == S[c:...

There are two independent bugs in the failing submissions, both visible from the error traces. First, the input is being parsed using input() or int(input()), assuming a clean token structure like: But the provided test input is heavily malformed from the program’s…

We are given a set of axis-aligned square obstacles placed on an infinite 2D grid. Each obstacle is fixed in position and cannot be crossed. On top of that, we have multiple queries involving a moving square “agent” of fixed side length per query.

We are given a grid where some cells contain trees and others are empty ground. The goal is to assign a “day number” to every tree cell such that all trees are eventually removed, and the schedule respects a key constraint: a tree can only be removed on a day if it is…

We are working with a system of coffee types where each type behaves like a convertible resource. The goal is to end up with as much coffee of type 1 as possible. Initially, Kanako receives a controllable amount of coffee from Sumika.

We are given several types of coffee, but only type 1 is valuable in the end. The process has two stages. First, we can obtain some initial coffee from Sumika. She can provide any non-negative real amount of coffee, but only for types marked with a 1 in a binary string.

We are tracking a sequence of moments when a person checks a clock. Each check happens at a time determined by a recurrence, starting from an initial delay and then evolving based on the previous check time and a small periodic function of the step number.

We are growing a tree one node at a time. Initially there is a single vertex. Each query attaches a new node to an existing node, so after $i$ queries we have a rooted structure with $i+1$ vertices connected in a tree.

We are given two collections of scores, one for each semester. Each semester’s grade is simply the arithmetic mean of its scores, and the final grade is the average of the two semester means.

We are given an $n times n$ grid where some cells already have fixed integer values and the rest are unknown. The final grid we want to imagine completing must satisfy a very rigid geometric rule: every pair of edge-adjacent cells must differ in value by exactly 1.

We are given a line of fanclubs placed on a number line. Each fanclub sits at a distinct coordinate and contains either one or two members.

We are trying to assign coins to six distinct cows so that each cow receives exactly one coin and the total value of all assigned coins equals a target sum $n$.

We are given a collection of segments on a number line, each segment representing an interval $[li, ri]$. From these intervals, we want to choose as many as possible such that all chosen intervals share at least one common point.

We are given a sequence of monthly sales values and a fixed window size $K$. For every contiguous segment of length $K$, we compute its average sales. Since all windows have the same length, comparing averages is equivalent to comparing sums.

We are given a sequence of 2N coin values arranged in a line. Two players alternately remove exactly one coin per move, choosing either the leftmost or rightmost remaining coin. Technoblade moves first, Skeppy moves second, and they continue until all coins are taken.

We are maintaining an array of values over time, where each position represents a plot of land. The array changes through range updates that add a value to all elements in a segment.

We are given a circular arrangement of $n$ players, each player belongs to some country $pi$. The circle means that player $1$ is adjacent to player $n$, and otherwise adjacency follows the natural order.

We are counting colorings of a circular structure. For a fixed length $K$, imagine $K$ positions arranged in a ring. Each position receives one of $M$ jewel types, and two jewels of different types are always distinguishable while identical types are indistinguishable.

We are given a sequence of monthly sales values and a fixed window size $K$. For every contiguous segment of length $K$, we compute its average sales. Since all windows have the same length, comparing averages is equivalent to comparing sums.

We are asked to count how many different purchase plans achieve an exact total number of potatoes, where each store sells fixed-size packages. For store i, every package contributes bi potatoes, and we choose a nonnegative number of packages from each store.

We are given a grid that represents a Skywars map. Some cells already contain terrain blocks, some are empty, and exactly one cell marks Techno’s position while exactly two cells mark enemy positions.

We are given a sequence of monthly sales values and a fixed window size $K$. For every contiguous segment of length $K$, we compute its average sales. Since all windows have the same length, comparing averages is equivalent to comparing sums.

Two players each start with a fixed number of potatoes and then grow more potatoes at a constant daily rate. Technoblade starts with $X1$ potatoes and gains $Y1$ potatoes per day. His rival starts with $X2$ potatoes and gains $Y2$ potatoes per day.

We are given a single integer $n$, and we are asked to compute the sum of the first $n$ odd numbers. In other words, we conceptually build a sequence starting from 1, increasing by 2 each time, and stopping after $n$ terms. The task is to return the total of that sequence.

We are given a rectangular farm grid and a sequence of operations that affect it over time. The first type of operation repeatedly tills subrectangles, increasing a counter on every cell inside the chosen region.

We are given a set of points on the plane, each point carrying a positive value interpreted as an amount of oil. Alice may choose some subset of these points and draw a closed boundary around them.

We are working with a binary matrix of size $2 times n$, meaning there are two rows and $n$ columns, and every cell contains either 0 or 1.

We are given several independent random experiments, each described by an interval. For each interval $[li, ri]$, one real number is sampled uniformly at random. We repeat this for all testers, so we end up with a set of $n$ independent random values.

We are given several test cases, and each test case consists of a collection of closed intervals on a number line. Every interval must be assigned to exactly one of two groups.

This failure is much simpler than it looks: the program is now crashing at the very first line. That means the submitted code uses: but never imported sys in that version of the script.

We are given a sequence of axis-aligned rectangles. Each rectangle represents a gift, and it is already sorted by its right boundary in non-decreasing order.

We are given a rooted tree where every node starts with an initial color and must end with a target color. The only operation allowed is to choose a node and paint its entire subtree with a single chosen color.

We are given a cyclic schedule with $N$ days, where meetings happen on some subset of days in every cycle. Each of the $M$ problem setters has a fixed weekly pattern: setter $i$ attends meetings on $pi$ specific days of the cycle. Now imagine an idea appears on some day $d$.

We are working with permutations of the numbers from 1 to n, but the actual object of interest is not the permutation itself, rather all of its contiguous subarrays, and how they behave under two statistics computed on the values inside them.

We are counting structured compositions of an integer $n$, but with two extra constraints layered on top. Each valid object is a sequence of positive integers whose sum is exactly $n$, and the sequence must read the same forwards and backwards.

We are given two arrays of the same length. One array, call it a, is fixed in position. The second array, b, can be permuted arbitrarily.

Each query gives three numbers $x$, $y$, and $z$. We are allowed to choose an integer $v$ in the range $0 le v < z$. For that chosen $v$, we evaluate two shifted values $x+v$ and $y+v$, take their bitwise XOR, and want the maximum possible value over all valid $v$.

We are processing a sequence of values in a fixed order. A score starts at zero, and for each value in the sequence we must immediately decide whether to add it to the current score or multiply the current score by it.

We are given a hidden positive integer $x$, and we are allowed to ask questions about it in the form of clues. Each clue chooses two integers $a$ and $b$, and we are told whether the absolute difference $ The goal is not to compute $x$ by interactive querying, but to design a…

We are given a string over lowercase English letters and we are allowed to delete characters in any positions while keeping the remaining characters in order. Among all possible subsequences that form a palindrome, we need to pick the one that is lexicographically largest.

Each query describes a range of integers from l to r, and asks how many ordered pairs (a, b) inside that range satisfy a specific condition involving a function f(a, b). The function itself simplifies before we even start counting pairs.

We are given a stack of distinct integers, where the first element is the bottom and the last element is the top.

The task is deliberately minimal: the judge gives us a single integer input, but the actual computation is not derived from that value in any meaningful way. Instead, the problem is essentially asking us to output a fixed name from a known set of nine possible strings.

We are given a square grid of size $(2n+1) times (2n+1)$ with a distinguished center cell. All cells whose Manhattan distance from the center is between 1 and $n$ are considered active cells, called petals. The center cell itself is not part of the region we need to cover.

This failure is not algorithmic. It is purely an input parsing bug. The program assumes every test input begins with: But the failing input is: So the first token is already part of a test case, not the number of test cases.

Two people start outside a line of asteroids: Jesse starts just before the first asteroid, and Jerry starts just after the last one. Each asteroid has a fixed size, and both players move step by step toward each other until they end up on the same asteroid.

We are given a rooted tree where every node contains a panda, and all pandas must eventually travel toward the root along unique tree paths.

We are given a function that transforms a positive integer by repeatedly taking its decimal prefixes and summing them.

We are given an array of integers, and we are allowed to repeatedly perform a very specific transformation: pick two different positions in the array and pick an integer mask x, then apply XOR with x to both selected elements.

We are building a binary string of length n, and we want it to differ from its reverse in exactly k positions. For each position i, we compare the character at i with the character at its mirrored position n-i+1.

We are given a set of red pandas, but instead of knowing their positions on the line, we are only given how far apart each pair of pandas is. Separately, we are also given a sorted list of actual coordinates on the number line.

We are given a small integer $x$, and we are allowed to add another integer $y$ where $0 le y le 100$. From this shifted value $n = x + y$, we compute two numbers: $n^2$ and $n^3$.

This failure is a direct consequence of the previous “mode-splitting” fix being incorrect. Your program is now doing this: If input has 2 integers → treat as arithmetic problem and print derived formula Otherwise → treat as stack simulation For the input: you…

We start with a collection of stacks, each stack having a fixed capacity of $m$. Initially, stacks $1$ through $n-1$ are perfectly uniform: stack $i$ contains exactly $m$ blocks, and every block inside it carries label $i$. The last stack is empty.

We are given a tree with an even number of nodes, so every node belongs to exactly one friend pair. Each pair connects two nodes, and we can think of it as a fixed relationship that travels through the tree along the unique simple path between those nodes.

We are given a square grid of size $(2n+1) times (2n+1)$ with a single distinguished center cell. All cells whose Manhattan distance from the center is between 1 and $n$ form a “ringed diamond” shape, and every such cell must be covered exactly once.

We are given a line of pumpkins. Each pumpkin has two attributes: a value that we gain if we eat it, and a radius that determines how far its “light” spreads when we carve it. Over time, we process a fixed sequence of operations indexed from 1 to n.

We are given a rooted tree, and each edge carries a weight that defines how likely a process moves through that edge. The process starts at the root. Whenever we “activate” a node, we spend one unit of cost, and that node becomes empty.

This is no longer a logic bug. It is a hard input-structure mismatch combined with incorrect consumption of the input stream. The crash: means: your parser assumes more integers exist than were actually provided.

We are given a rooted tree where every node initially hosts a single panda. The goal is to release pandas over time so that they all eventually move upward toward the root, one step per second once released. A panda at the root does not move further but still counts as released.

We are given an array a of length n. We are allowed to change some of its elements. After these changes, we want the array to be compatible with the existence of another array b of length n+1, where every value in a is defined as the maximum of two adjacent values in b.

We are working with a transformation from integers to other integers, defined through decimal representation. Take any positive integer and look at all of its prefixes in base 10. Each prefix is formed by cutting the number from the right side, keeping at least one digit.

We are given a starting integer $x$, and we are allowed to adjust it by choosing a small integer $y$ between 0 and 100. After choosing $y$, we compute the number $n = x + y$, then form two values: $n^2$ and $n^3$.

We are given a tree with up to three hundred thousand nodes. The first part of the nodes are special locations called exhibits, and the remaining nodes are feeding stations, each carrying a fixed food color. Red pandas travel along shortest paths between pairs of nodes.

We are given a directed graph that forms a rooted structure starting from city 1, since every city is reachable from city 1. Each city has a fixed cereal price, and Larry may buy cereal only at cities he visits.

We are asked to design a grid of size at most $64 times 64$, then place obstacles in some cells so that the number of valid monotone paths from the top-left corner to the bottom-right corner equals a given integer $k$, possibly up to $10^{18}$.

Your current output already shows something important: the move count is correct, but the structure of moves is wrong in a systematic way, not random. Compare expected vs actual: Expected begins with: Actual begins with: So two concrete bugs are visible: 1.

The amusement park is a tree where each node represents a ride. Visiting a ride for the first time grants a fixed enjoyment value, but only if the ride is operational on the current day. Each ride has a periodic schedule: it is open only on days that are multiples of its period.

We are given an array of length $n$, initially all zeros, together with a dynamic set of special positions called marked indices. The set changes over time through toggle operations. At any moment, a position is either in this marked set or not. There are two kinds of operations.

We are given an array and a rule that allows us to erase any contiguous segment as long as two conditions hold. The segment must have length at least two, and the values inside it must be “tight” in the sense that the difference between its maximum and minimum is at most $k$.

We are given several stacks of blocks. Each stack has a capacity limit, and blocks can only be moved one at a time from the top of one stack to the top of another.

We are given a tree rooted at node 1, and each node initially contains exactly one panda. Over time, we “release” pandas from their home nodes. Once released, a panda moves upward toward the root, advancing exactly one edge per second.

We are working with a transformation on positive integers. Given a number $x$, we write it in base 10 and repeatedly take prefixes from the left: the full number, then everything except the last digit, then everything except the last two digits, and so on until a single digit…

This failure is no longer about the algorithm or even parsing logic. It is a pure implementation error introduced in the previous “fix”. The traceback is explicit: So the code uses: without importing sys. That is the immediate crash.

A line of people is served sequentially by a water dispenser. Each person has a demand in liters, and a single water bucket on the dispenser contains a fixed capacity of $C$ liters. People are served one after another using the current bucket until it runs out.

We are given a permutation of numbers from 1 to n, and we are allowed to reorder them arbitrarily. For any chosen ordering, we compute a score by pairing each position i with the value placed there and taking the bitwise XOR of the two, then summing these values across all…

We are given a long array of integers and many queries on subsegments. For any interval inside the array, we call it “good” if that segment contains at least one even number and at least one odd number.

We are given a two-player deterministic card game played with perfect information. Each player starts with their own hand of $n le 13$ cards, and all cards are known to both players. Every card has a suit among four types and a rank from 2 up to Ace.

We are given a string of length $n$ consisting of three types of characters: open brackets, close brackets, and wildcard characters. Each wildcard can later be turned into either an open or a close bracket.

We are asked to count how many sequences of length n we can build using integers from 1 to m, with the restriction that every pair of adjacent elements must be coprime.

We are given a line of cats labeled from 1 to n. Each cat wants to fight with every other cat except its immediate neighbors on the line. So cat i wants fights with all j such that the distance A fight does not happen directly in pairs one by one. Instead, we schedule rounds.

We are counting how many integers lie in the range from 0 up to but not including $10^n$, with the extra requirement that each chosen number is divisible by a fixed integer of the form $3 cdot 2^a$.

This failure is no longer about the algorithm or even parsing logic. It is a pure implementation error introduced in the previous “fix”. The traceback is explicit: So the code uses: without importing sys. That is the immediate crash.

We are given a sequence of days, each day having a base cost for buying coffee. We are also given a collection of coupons. Each coupon has a deadline day and a discount value.

We are given a connected undirected simple graph on $n$ labeled vertices, with the restriction that no vertex is allowed to have degree larger than 3. Among these vertices, exactly $k$ of them must have degree exactly 3, while every other vertex must have degree at most 2.

We are given an undirected tree where some nodes may contain hamsters. Each hamster is not static, it keeps moving forever.

Each participant starts at a fixed point in the plane, and we are asked to choose a single meeting point such that every participant travels the same Euclidean distance from their start to this shared destination.

This crash happens before any algorithm runs, so the logic is not the issue. The failure is purely input parsing.

We are given a number $n$, and for each test we must output two positive integers $a$ and $b$ such that their product equals $n$. The extra constraint is that neither $a$ nor $b$ is allowed to end in a zero in decimal representation.

We start from a clean permutation containing the numbers from 1 to n. A segment of consecutive positions is selected, and every value inside that segment is multiplied by the same unknown integer x.

We are given aggregated survey statistics from a questionnaire where each participant could tick multiple options. There are $n$ listed programming language options, plus an additional implicit option called “other”.