Description

[[Category: Simulation]]

Your task is to graph the price of a stock over time. In one unit of time, the stock can either Rise, Fall or stay Constant. The stock's price will be given to you as a string of R's, F's and C's. You need to graph it using the characters '/' (slash), '\' (backslash) and '_' (underscore).

Input

The first line of input gives the number of cases, N (N<=100). N test cases follow. Each one contains a string of at least 1 and at most 50 upper case characters (R, F or C).

Output

For each test case, output the line "Case #x:", where x is the number of the test case. Then print the graph, as shown in the sample output, including the x- and y-axes. The x-axis should be one character longer than the graph, and there should be one space between the y-axis and the start of the graph. There should be no trailing spaces on any line. Do not print unnecessary lines. The x-axis should always appear directly below the graph. Finally, print an empty line after each test case.

Sample Input

3
RCRFCRFFCCRRC
RCRFCRFFCCRR
FFF

Sample Output

Case #1:
|             _
|  _/\_/\    /
| /      \__/
+---------------

Case #2:             
|  _/\_/\    /
| /      \__/
+--------------

Case #3:
| \
|  \
|   \
+-----

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Sample Output  Download

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Description

[[Category: Graph & DFS]]

You might have noticed that English and Spanish are spoken in many areas all over the world. Now it would be nice to rank all languages according to the number of states where they are spoken. You’re given a map which shows the states and the languages where they are spoken. Look at the following map:

ttuuttdd
ttuuttdd
uuttuudd
uuttuudd

The map is read like this: Every letter stands for a language and states are defined as connected areas with the same letter. Two letters are “connected” if one is at left, at right, above or below the other one. So in the above map, there are three states where the language “t” is spoken, three where “u” is spoken and one state where people speak “d”. Your job is to determine the number of states for each language and print the results in a certain order.

Input

The first line contains the number of test cases N. Each test case consists of a line with two numbers H and W, which are the height and the width of the map. Then follow H lines with a string of W letters. Those letters will only be lowercase letters from ‘a’ to ‘z’. 

1<= H, W <=100

N<=100

Output

For each test case print "World #n", where n is the number of the test case. After that print a line for each language that appears in the test case, which contains the language, a colon, a space and the number of states, where that language is spoken. These lines have to be ordered decreasingly by the number of states. If two languages are spoken in the same number of states, they have to appear alphabetically, which means language "i" comes before language "q", for example.

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[[Category: Euler Circuit]]

A catenym is a pair of words separated by a period such that the last letter of the first word is the same as the first letter of the second. For example, the following are catenyms:

dog.gopher
gopher.rat
rat.tiger
aloha.aloha
arachnid.dog

A compound catenym is a sequence of three or more words separated by periods such that each adjacent pair of words forms a catenym. For example,

aloha.aloha.arachnid.dog.gopher.rat.tiger

Given a dictionary of lower case words, you are to find a compound catenym that contains each of the words exactly once.

Input

The first line of standard input contains t (t<=100), the number of test cases. Each test case begins with 3 ≤ n ≤ 1000 - the number of words in the dictionary. n distinct dictionary words follow; each word is a string of between 1 and 20 lowercase letters on a line by itself.

Output

For each test case, output a line giving the lexicographically least compound catenym that contains each dictionary word exactly once. Output  '***' if there is no solution.

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[[Category: Single Source Shortest Path]]

Did you know that you can use domino bones for other things besides playing Dominoes? Take a number of dominoes and build a row by standing them on end with only a small distance in between. If you do it right, you can tip the first domino and cause all others to fall down in succession (this is where the phrase ``domino effect'' comes from).

While this is somewhat pointless with only a few dominoes, some people went to the opposite extreme in the early Eighties. Using millions of dominoes of different colors and materials to fill whole halls with elaborate patterns of falling dominoes, they created (short-lived) pieces of art. In these constructions, usually not only one but several rows of dominoes were falling at the same time. As you can imagine, timing is an essential factor here.

It is now your task to write a program that, given such a system of rows formed by dominoes, computes when and where the last domino falls. The system consists of several ''key dominoes'' connected by rows of simple dominoes. When a key domino falls, all rows connected to the domino will also start falling (except for the ones that have already fallen). When the falling rows reach other key dominoes that have not fallen yet, these other key dominoes will fall as well and set off the rows connected to them. Domino rows may start collapsing at either end. It is even possible that a row is collapsing on both ends, in which case the last domino falling in that row is somewhere between its key dominoes. You can assume that rows fall at a uniform rate.

Input

The input file contains descriptions of several domino systems (<=100). The first line of each description contains two integers: the number n of key dominoes ( 1<=n<=500 ) and the number m of rows between them. The key dominoes are numbered from 1 to n. There is at most one row between any pair of key dominoes and the domino graph is connected, i.e. there is at least one way to get from a domino to any other domino by following a series of domino rows.

The following m lines each contain three integers a, b, and l, stating that there is a row between key dominoes a and b (a!=b) that takes l (1<=l<=1000)seconds to fall down from end to end.

Each system is started by tipping over key domino number 1.

The file ends with an empty system (with n = m = 0), which should not be processed.

Output

For each case output a line stating the number of the case ('System #1', 'System #2', etc.). Then output a line containing the time when the last domino falls, exact to one digit to the right of the decimal point.

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Sample Output  Download

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