Mr. AH got his special name from his favorite game, which is called On the Road to Happiness. This game is played with a string s consisting of n uppercase English letters, b beautiful cards, and a magical wand.

A beautiful card 'x y c' can be used to swap the letters in positions x and y after paying c coins. Mr. AH can use every beautiful card infinitely, but he must pay each time he wants to use it.

Some of the beautiful cards are interesting, a beautiful card 'x y c' is said to be interesting if Mr. AH cannot move the letter in position x to position y (or the letter in position y to position x) using any sequence of cards unless this card is among them.

The magical wand allows Mr. AH to use the beautiful cards without paying anything, except for the interesting cards, Mr. AH must respect these cards and pay for using them. Mr. AH can use the wand as much as he needs.

A position in the given string is said to be happy if it initially contains the letter 'A'. The goal of the game is to find the minimum cost to move all letters 'H' in the string to the happy positions, such that each happy position can contain at most one 'H' letter.

Mr. AH thinks that he is the king of this game, but he wants to see other players play it to prove that. So Mr. AH asked you to play the game, can you?

It is your first day in your new job and guesses what, your first task is already waiting for you! Your task is to build a memory management system.

In this system, the memory will consist of $$$m$$$ bytes ordered from $$$1$$$ to $$$m$$$. Originally, there are $$$n$$$ files in the system, such that the $$$i^{th}$$$ file is occupying all bytes from $$$l_i$$$ to $$$r_i$$$ (inclusive). It is guaranteed that no two files share the same memory position (byte).

The main goal of the system is to answer multiple queries such that each query consists of a file of size $$$k$$$ bytes, and the system must determine if there exist at least $$$k$$$ consecutive bytes that can be reserved and assigned to that file.

Formally, at the $$$j^{th}$$$ query, you are given an integer $$$k_j$$$ and your task is to find a pair of integers $$$l_j$$$ and $$$r_j$$$, such that:

• All bytes between $$$l_j$$$ and $$$r_j$$$ (inclusive) are free (not occupied).
• $$$r_j - l_j + 1 \geq k_j$$$.
• If there are multiple solutions, find the one with the maximum $$$r_j$$$. If there are still multiple solutions, find the one with maximum $$$l_j$$$.
• If the $$$j^{th}$$$ file cannot be saved in the system, both $$$l_j$$$ and $$$r_j$$$ must be $$$-1$$$.

Please note that you are not reserving the bytes for the files in the queries, you are just checking if there exists an empty space for the file in the system. So, an empty byte in the system can be assigned to multiple queries files. However, if a byte is originally occupied in the system, you cannot use it for the queries files.

This problem is very simple so the problem setters decided that its statement should be simple too. You are given two integers $$$n$$$ and $$$m$$$ such that $$$\text{gcd}(n,\,m) \equiv 1$$$, and your task is to find the value of the function $$$\text{F}(n,\,m)$$$ as follows:

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For example, the gcd of $$$8$$$ and $$$12$$$ is $$$4$$$.

A bitwise XOR takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is $$$1$$$ if both bits are different (only one of them is $$$1$$$ and the other is $$$0$$$), but will be $$$0$$$ if both bits are the same (both are $$$0$$$ or both are $$$1$$$). For example, the bitwise XOR of the patterns $$$0101$$$ and $$$1100$$$ is $$$1001$$$.

In this problem, you are given $$$3$$$ binary strings of lengths $$$10$$$ digits such that all digits are either $$$0$$$ or $$$1$$$. You can swap any two digits in the same string infinitely, but you cannot swap two digits from two different strings.

Your task is to rearrange digits in the given strings in a way such that the bitwise XOR of the strings after rearranging their digits is as largest as possible. Can you?

You are given a string $$$s$$$ of length $$$n$$$ consisting of lowercase English letters. This string can be used to build other strings. The cost of each letter in $$$s$$$ is given by another string $$$c$$$ of length $$$n$$$ consisting of digits, such that the cost of using the letter $$$s_i$$$ is $$$c_i$$$ coins.

Also, you are given another string $$$p$$$ of length $$$m$$$ consisting of unique lowercase English letters. Your task is to find the minimum cost to build string $$$p$$$ by using the letters of $$$s$$$. Can you?

Camel case is a naming convention practice for multi-word identifiers in programming languages. In this practice, each word except for the first word will begin with an uppercase letter, with no intervening spaces or punctuation.

For example, "problem", "contestName", and "contestStartingTime" are all following the camel case practice, while "Server", "ProblemName", and "first-Place" are not.

in this problem, you are given a variable name that is following the camel case naming practice, and your task is to determine if the variable name is accepted or not. A variable name is accepted if it is consisting of no more than $$$7$$$ words.

Assem bought a new chess board that has a special king that move in a different way than other regular kings.

In one move, the special king can move from its position in one of the following directions: up, down, left, or right. Formally, if the special king is standing on position ($$$x$$$, $$$y$$$), in one move it can go to one of the following positions: ($$$x - 1$$$, $$$y$$$), ($$$x + 1$$$, $$$y$$$), ($$$x$$$, $$$y - 1$$$), or ($$$x$$$, $$$y + 1$$$).

Initially, the special king is standing on position ($$$x_1$$$, $$$y_1$$$) and Assem wants to place it on position ($$$x_2$$$, $$$y_2$$$). Can you help Assem by calculating the minimum number of required moves he needs to accomplish his goal?

Have you ever heard about the universal string? This is the largest string in the world, and it is the mother of all strings that will ever exist in any programming language!

The universal string is an infinite string built by repeating the string "abcdefghijklmnopqrstuvwxyz" infinitely. So, the universal string will look like this:

You are given a string $$$p$$$ and your task is to determine if $$$p$$$ is a substring of the universal string. Can you?

A substring of $$$s$$$ is a non-empty string $$$x$$$ = $$$s$$$[$$$l$$$$$$\dots$$$ $$$r$$$] = $$$s_l$$$$$$s_{l+1}$$$$$$\dots$$$ $$$s_r$$$ (1 $$$\le$$$ $$$l$$$ $$$\le$$$ $$$r$$$ $$$\le$$$ |$$$s$$$|). For example, "code" and "force" are substring of "codeforces", while "coders" is not.

You are given an array $$$a$$$ of $$$n$$$ integers, and an integer $$$k$$$. You have to make $$$k$$$ negation operations such that at each operation you need to choose an element $$$a_i$$$ from the array and replace it with $$$-a_i$$$.

Your task is to find the optimal way to make the $$$k$$$ negation operations such that at the end the sum of the array $$$a$$$ is as maximal as possible. Can you?

You are given a grid $$$g$$$ consisting of $$$n$$$ rows each of which is divided into $$$m$$$ columns.

You can swap any two integers in the same row infinitely, but you cannot swap two integers from two different rows.

Your task is to maximize the beauty of the grid by rearranging integers in each row. The beauty of the grid is the number of pairs ($$$i,\,j$$$) ($$$1 \lt i \le n,\, 1 \le j \le m$$$) such that $$$g_{i,j}$$$ is equal to $$$g_{i-1,j}$$$ (i.e. $$$g_{i,j} \equiv g_{i - 1,j}$$$).

A bitwise OR takes two equal-length binary representations and performs the logical OR operation on each pair of the corresponding bits. The result in each position is $$$0$$$ if both bits are $$$0$$$, while otherwise, the result is $$$1$$$. The bitwise OR operation is represented in this problem, and also in programming languages such as C++ and Java, using the operator "|".

To get the value of $$$x\,|\,y$$$, consider both numbers in the binary representation (padded with zeros to make their lengths equal), then apply the OR operation on the corresponding bits, and return the result into decimal form. For example, the result of $$$10\,|\,17$$$ = $$$01010\,|\,10001$$$ = $$$11011$$$ = $$$27$$$.

You are given an array $$$a$$$ of $$$n$$$ integers. A subarray of the array $$$a$$$ is a sequence $$$a_l, a_{l + 1}, \cdots, a_r$$$ for some integers ($$$l,\,r$$$) such that $$$1 \le l \le r \le n$$$.

The subarray OR is defined as the the bitwise OR of all elements inside that subarray. Formally, the subarray OR of the subarray ($$$l,\,r$$$) is $$$a_l\,|\,a_{l + 1}\,|\,\cdots\,|\,a_r$$$.

Your task is to find the subarrays OR values of all subarrays in the given array and return the number of unique values among them. Can you?

You are given a grid $$$g$$$ consisting of $$$n$$$ rows each of which is divided into $$$m$$$ columns. The grid contains unique values between $$$1$$$ and $$$n \times m$$$ (inclusive).

Also, you are given two values $$$h$$$ and $$$w$$$, and your task is to find the smallest median value that can be found in a rectangle of size $$$h \times w$$$.

A rectangle of size $$$h \times w$$$ is a rectangle consisting of $$$h$$$ rows and $$$w$$$ columns such that its top left corner is at a cell ($$$a,\,b$$$) and its right bottom corner is at a cell ($$$c,\,d$$$), and the following conditions are satisfied: ($$$c - a + 1 \equiv h$$$) and ($$$d - b + 1 \equiv w$$$).

The median of a set of numbers is the middle element in the sorted list of the given set. For example, the median of $$$\{2, 1, 3\}$$$ is $$$2$$$ and the median of $$$\{4, 2, 3, 1, 5\}$$$ is $$$3$$$.