Madison is a little girl who is fond of toys. Her friend Mason works in a toy manufacturing factory. Mason has a 2D board A of size with H rows and W columns. The board is divided into cells of size with each cell indicated by its coordinate (i,j). The cell (i,j) has an integer A_ij written on it. To create the toy Mason stacks A_ij number of cubes of size on the cell (i, j).

Given the description of the board showing the values of A_ij and that the price of the toy is equal to the 3d surface area find the price of the toy.

There is a strange counter. At the first second, it displays the number 3. Each second, the number displayed by decrements by 1 until it reaches 1. In next second, the timer resets to 2 X the initial number for the prior cycle and continues counting down. The diagram below shows the counter values for each time t in the first three cycles:

Find and print the value displayed by the counter at time t.

Happy Ladybugs is a board game having the following properties:

• The board is represented by a string, b, of length n. The i^th character of the string, b[i], denotes the i^th cell of the board.
  • If b[i] is an underscore (i.e., _), it means the i^th cell of the board is empty.
  • If b[i] is an uppercase English alphabetic letter (ascii[A-Z]), it means the i^th cell contains a ladybug of color b[i].
  • String b will not contain any other characters.
• A ladybug is happy only when its left or right adjacent cell (i.e., ) is occupied by another ladybug having the same color.
  In a single move, you can move a ladybug from its current position to any empty cell.
  Given the values of and for games of Happy Ladybugs, determine if it’s possible to make all the ladybugs happy. For each game, return YES if all the ladybugs can be made happy through some number of moves. Otherwise, return NO.

Given an array of strings of digits, try to find the occurrence of a given pattern of digits. In the grid and pattern arrays, each string represents a row in the grid. For example, consider the following grid:

1
2
3
4
5

1234567890
09**876543**21
11**111111**11
11**111111**11
2222222222

The pattern array is:

1
2
3

876543
111111
111111

The pattern begins at the second row and the third column of the grid and continues in the following two rows. The pattern is said to be present in the grid. The return value should be YES or NO, depending on whether the pattern is found. In this case, return YES.

Manasa is out on a hike with friends. She finds a trail of stones with numbers on them. She starts following the trail and notices that any two consecutive stones’ numbers differ by one of two values. Legend has it that there is a treasure trove at the end of the trail. If Manasa can guess the value of the last stone, the treasure will be hers.

You are given a square map as a matrix of integer strings. Each cell of the map has a value denoting its depth. We will call a cell of the map a cavity if and only if this cell is not on the border of the map and each cell adjacent to it has strictly smaller depth. Two cells are adjacent if they have a common side, or edge.

Find all the cavities on the map and replace their depths with the uppercase character X.

You are the benevolent ruler of Rankhacker Castle, and today you’re distributing bread. Your subjects are in a line, and some of them already have some loaves. Times are hard and your castle’s food stocks are dwindling, so you must distribute as few loaves as possible according to the following rules:

1. Every time you give a loaf of bread to some person i, you must also give a loaf of bread to the person immediately in front of or behind them in the line (i.e., persons i + 1 or i - 1).
2. After all the bread is distributed, each person must have an even number of loaves.

Given the number of loaves already held by each citizen, find and print the minimum number of loaves you must distribute to satisfy the two rules above. If this is not possible, print NO.

For example, the people in line have loaves B = [4,5,6,7]. We can first give a loaf to i = 3 and i = 4 so B = [4,5,7,8]. Next we give a loaf to i = 2 and i = 3 and have B = [4,6,8,8] which satisfies our conditions. We had to distribute 4 loaves.

Flatland is a country with a number of cities, some of which have space stations. Cities are numbered consecutively and each has a road of 1km length connecting it to the next city. It is not a circular route, so the first city doesn’t connect with the last city. Determine the maximum distance from any city to it’s nearest space station.

For example, there are n = 3 cities and m = 1 of them has a space station, city 1. They occur consecutively along a route. City 2 is 2 - 1 = 1 unit away and city 3 is 3 - 1 = 2 units away. City 1 is 0 units from its nearest space station as one is located there. The maximum distance is 2.

Lisa just got a new math workbook. A workbook contains exercise problems, grouped into chapters. Lisa believes a problem to be special if its index (within a chapter) is the same as the page number where it’s located. The format of Lisa’s book is as follows:

• There are n chapters in Lisa’s workbook, numbered from 1 to n.
• The i^th chapter has arr[i] problems, numbered from 1 to arr[i].
• Each page can hold up to k problems. Only a chapter’s last page of exercises may contain fewer than k problems.
• Each new chapter starts on a new page, so a page will never contain problems from more than one chapter.
• The page number indexing starts at 1.

Given the details for Lisa’s workbook, can you count its number of special problems?

For example, Lisa’s workbook contains arr[1] = 4 problems for chapter 1, and arr[2] = 2 problems for chapter 2. Each page can hold k = 3 problems. The first page will hold 3 problems for chapter 1. Problem 1 is on page 1, so it is special. Page 2 contains only Chapter 1, Problem 4, so no special problem is on page 2. Chapter 2 problems start on page 3 and there are 2 problems. Since there is no problem 3 on page 3, there is no special problem on that page either. There is 1 special problem in her workbook.

Note: See the diagram in the Explanation section for more details.

Calvin is driving his favorite vehicle on the 101 freeway. He notices that the check engine light of his vehicle is on, and he wants to service it immediately to avoid any risks. Luckily, a service lane runs parallel to the highway. The service lane varies in width along its length.

You will be given an array of widths at points along the road (indices), then a list of the indices of entry and exit points. Considering each entry and exit point pair, calculate the maximum size vehicle that can travel that segment of the service lane safely.

For example, there are n = 4 measurements yielding width = [2,3,2,1]. If our entry index, i = 1 and our exit, j = 2, there are two segment widths of 2 and 3 respectively. The widest vehicle that can fit through both is 2. If i = 2 and j = 4, our widths are [3,2,1] which limits vehicle width to 1.