Dear game programmers, what is the million-dollar puzzle of civilization and prosperity?

This million-dollar puzzle is an interview topic of Qingdao Wenming Shisheng Network Technology Co., Ltd. This company needs to recruit a large number of senior programmers to develop a new project, so it came up with such a problem, and it is said that the annual salary is one million. Only people who solve problems have the opportunity to interview. I posted a question for you to see if you have this million-dollar annual salary!

Puzzle content:

Super drink

Under the banner of civilization and prosperity, the chemical products laboratory has been studying how to formulate new stimulants that can improve the production efficiency of engineers and keep their heads clear. A series of compounds were separated, and when they were mixed with sugar water, they became the active ingredients of the next generation of super drinks.

These compounds are similar in composition: any compound can be changed into any other compound through a certain chemical reaction. The actual cost of chemical reaction is very low, but the cost of reaction equipment and catalyst is quite high. The equipment used to convert one compound into another must also be customized separately. Each piece of equipment will have a purchase cost, and one compound needs to be put in to produce another compound. The laboratory of the history of civilization must be equipped with sufficient equipment to ensure that it can produce a whole series of compounds no matter which compound can be bought in the market.

Write a program with only one command line parameter. This parameter must be a file name that contains the input data. The program should output the cheapest scheme to the standard output, so that Wenming Shisheng Company can use the source compound or multiple compounds to produce its beverage (see below for details). We assume that all chemicals mentioned in the equipment catalogue are necessary raw materials for preparing beverages. We can't guarantee that all chemical reactions can be completed in one step, but we can guarantee that any compound can be converted into any other compound through reaction. The puzzle results and program schemes submitted by the contestants must follow the following input and output specifications, otherwise they will be considered unqualified. The programs submitted by participants will be tested with different data in several device directories. In addition, the procedures submitted by participants must be fast and can give the correct solution within a few minutes.

Input specification

The input file needs to contain a list of available devices. Each line of the file represents a specific device model. The format of each line is as follows:

& lt machine name & gt& lt original compound & gt& lt new compound & gt& lt price & gt (corresponding Chinese means equipment name, source compound, new compound and price).

The device name should start with the letter "m" (without quotation marks) followed by a non-zero integer. The equipment name can be' m 1',' m2',' m 13' and so on.

The compound name should start with the letter "c" (without quotation marks) followed by a non-zero integer. The names of compound words can be C4, C6, C24 and so on.

Please use simple non-zero integers for prices, and do not use commas, periods or unit symbols (we assume that all prices are in US dollars). Such as' 987334','13948295' and so on.

Please separate paragraphs in the input file with spaces or tabs. The last item may or may not have spaces at the end of the line. Ensure that the submitted program can pass the running verification of the input file with correct data format.

Example of input file:

M 1 C 1 C2 2773 17

M2 C2 C 1 26247

M3 C 1 C3 478726

M4 C3 C 1 930382

M5 C2 C3 370287

M6 C3 C2 1 12344

Output specification

Please output in strict accordance with the following instructions: the participant's program must first output the total price of the required equipment (please do not insert commas, periods or any other symbols), and this total price should be expressed by a simple integer with a line at the end.

Then the program submitted by the participants needs to print the purchased equipment numbers, arrange them in ascending order and omit the identification character' m'. Equipment numbers must be separated by spaces. The program should start a new line after the last device number, and no spaces can be added.

Sample output (a new line is required at the end of each line)

6 173 17

2 3 6