Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

Continental drift refers to the idea that once the earth’s continents were all in one piece and with time they drifted away from each other and arrived at their present positions.

In this problem, we are concerned with the reverse process – Continental Coalesce.

For the sake of brevity, let’s assume the continents were initially merged together forming a square. With time, the square disintegrated into K different continents in the shape of rectangles and drifted away from its source.

You are provided with the current locations of the continents (i.e. rectangles). These locations were outlined with the help of satellites. Your first job is to figure out whether the data provided is a valid one. The data is valid if you can move the rectangles and form a square. In one move, you can pick any rectangle and push it one unit in one of the four directions (north, south, east or west). The continents can slide underneath one another during movement – meaning, more than one continent can occupy a particular position simultaneously. If it is possible to form a square then you are also required to find the minimum number of moves to do that. The final position of the square is not the primary concern here. Note that in the final position, two continents cannot overlap and the desired square cannot have any holes in it.

Input

The first line of input is an integer T (T <= 200) that indicates the number of test cases. Each case consists of 20 lines containing 20 characters. Each character can either be a dot(.) representing an empty space or an x (ASCII value 120). Every x character will be part of some continent.

Notes:

·         In the input grid, it’s guaranteed that, x characters from different continents will not be adjacent to each other. Any x character will be part of some rectangle

·         Two cells are adjacent if they share a common edge.

·         There will be exactly 25 x characters in the grid.

·         The number of continents, K, will be at most 5.

·         There is a blank line before the start of every case.

·         The rectangles and the desired square are axis parallel.

·         The earth here is flat. That is, the first and last row is NOT adjacent to each other. Same thing holds for the first and last column.

Output

For each case, output the case number first. If it’s not possible to form a square by moving the rectangles around, output “invalid data”, quotes for clarity. If it is possible, output the minimum number of moves required to complete the task.