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**Input File:** `streetin.txt`

**Output File:** `streetout.txt`

**Time Limit:** 1 second

**Memory Limit:** 1 GB

The great city of Dubvegas is designing one side of a new street. This street is divided into evenly sized chunks of land, each of which will be used for either a house or a park. The city takes great pride in both the number of parks that it has, and that no one has to walk far to reach one of their wonderful parks.

In particular, the city calls a group of consecutive houses a `block'. The size of a block is the number of houses it contains.

You must determine, given the number of chunks of land on the street and the number of parks that will be built, the minimum possible size of the largest block.

The only line will contain the number of chunks of land N on the street, followed by the number of parks that will be built K.

Your program should output the minimum possible size of the largest block on a street with N chunks of land, where K parks will be built.

**Input File:** `cloudin.txt`

**Output File:** `cloudout.txt`

**Time Limit:** 1 second

**Memory Limit:** 1 GB

During lunch you and your friends were playing your favourite game `stand along a line' when a huge cloud blew overhead. So you got to wondering, how long could that cloud have been? You immediately noted down how far apart each of your friends were standing from one another along the line, and the maximum number that were simultaneously underneath the cloud.

Note that if two people are exactly separated by the length of the cloud, then only one of them can be covered by the cloud at a time. Thus if a cloud is 5 metres long, and two people are standing 5 metres apart, the cloud is only able to cover one of them at a time.

You must now determine the maximum length the cloud could have been, taking into account the maximum number of people it covered simultaneously.

The first line will contain the number of people standing along the line, N, followed by the maximum number covered at any time by the cloud K.

The following N-1 lines contain the successive distances between the N people playing the game. These will always be integers.

The maximum length the cloud could have been given that it never covered more than K of your N friends.

**Input File:** `janitorin.txt`

**Output File:** `janitorout.txt`

**Time Limit:** 1 second

**Memory Limit:** 1 GB

Congratulations! You have been appointed head bathroom janitor of your school! Okay, okay, I know you're not thrilled, but somebody has to do it. We thank you for your sacrifice.

The bathroom floor is covered in a rectangular grid of tiles. No one is watching you very closely, so pouring a bucket of water over the floor is enough to make it look like you cleaned it. There is one small problem. The floor is uneven, so depending on which tile you pour the water on, some tiles may not become wet at all, and your deception will be exposed.

Water can flow from any square to any adjacent square of lower height, where adjacent squares may be to the north, south, east or west (water cannot flow across diagonals).

To finish your chore as soon as possible, you've decided to find out what is the fewest number of tiles you need to pour water on to make sure every tile becomes wet.

To complicate matters further, the bathroom is undergoing some hasty renovations. Each day, a tradie will replace one of the tiles, changing its height. After each replacement, you will need to figure out again how many tiles you need to pour water on.

- The first line of input contains three space-separated integers, R, C, and Q. There are R rows and C columns of tiles and there will be Q replacements made by the tradies.
- The next R lines each contain C space-separated integers, giving the initial heights of the tiles. The tradie did such a terrible job at tiling the bathroom that literally no two adjacent tiles have the same height, even after any replacements.
- The following Q lines each contain three integers r
_{i}, c_{i}and h_{i}. This indicates that the tradies have replaced the tile situated in row r_{i}and column c_{i}with a tile of height h_{i}. Rows are labelled from 1 to R (from top to bottom) and columns are labelled from 1 to C (from left to right).

The output should contain Q+1 lines. The first line should contain the fewest tiles you need to pour water on to make sure every tile gets wet before any replacements are made. The next Q lines should correspond to the Q tile replacements. After each replacement has been made (including all previous modifications), your program should write one line containing the fewest tiles you need to pour water on to make sure every tile gets wet.

**Input File:** `detectivein.txt`

**Output File:** `detectiveout.txt`

**Time Limit:** 1 second

**Memory Limit:** 1 GB

Congratulations on being the latest contestant on `Who Stole the Cookie?'. This is a game show where you, the contestant, are tasked with finding out who could have stolen a cookie from a cookie jar. Though because thieves are a dishonest bunch you may also conclude that you are being lied to.

You know that a single student committed the theft last night inside a dormitory with N children inside. Each child inside this dormitory is either a liar, or honest. A liar will always tell lies, and an honest child will always tell the truth. However, you do not know who is a liar and who is honest.

Since the theft, you have gathered M statements from the N children. These statements are all of the following form:

- A says B is honest.
- A says B is a liar.
- A says B stole the cookie.

Given all of these statements, to win the game you must determine everyone who could have possibly stolen the cookie, or if the statements you received are inconsistent.

The first line of input contains two integers, the number of children in the dormitory N and the number of statements you have gathered M.

The following M lines all contain three integers. The first integer is the number of the child making the statement (Child A). The second integer is the number of the child that the statement is being made about (Child B). The third integer indicates what type of statement is being made about child B, and these are given by the following:

- The integer
`1`indicates that child A claims that child B is honest. - The integer
`2`indicates that child A claims that child B is a liar. - The integer
`3`indicates that child A claims that child B stole the cookie.

You are guaranteed that no line of input will be repeated, and that a child will never make a claim about themselves.

To win the prize, you must output the numbers of all children who could have stolen the cookie in ascending order. If there are no children who could have stolen the cookie, or there is an inconsistency in their statements then output the word `MISTAKE`.

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