Problem C. Code Formatting ≡

Statement

Programmers are known to wage religious wars when issues of proper code formatting are discussed. When new team of programmers starts working on a project, it often brings slightly different code formatting style and wants to reformat old source code according to their own style. Moreover, inexperienced programmers often neglect the importance of good and consistent code style, thus complicating the work of their teammates and themselves. This situation creates thriving market for code formatting tools.

You are taking part in a proof-of-concept project for a new code formatting tool code named Salvation. This is only a pilot project aimed not for a practical usefulness, but to demonstrate your ability to parse and format code of a high-level language. Your task is to write code formatter for a language called TRIVIAL (The Rival Implementation-Agnostic Language). This language has trivial lexical and grammatical structures. It does not have any keywords and control structures, because all constructs of the language are represented as function calls and closures.

The lexical structure consists of identifiers, opening and closing parenthesis and curly braces, commas, and semi-colons. Identifiers consist only of digits '0'--'9' and Latin letters 'a'--'z', 'A'--'Z'. Lexical terms may be separated by whitespaces, leading and trailing whitespaces in the file are also allowed. Whitespace may consist of spaces, tab characters (ASCII code 9), and line separators (a pair of ASCII 13, 10).

The structure of the valid trivial program is derived from the following productions:

Properly formatted trivial program additionally conforms to the following rules:

• There are no empty lines.
• Tab characters are not used.
• The first character of the file is opening curly brace '{' (no preceding whitespaces), and the last character of the file is closing curly brace '}' (no trailing whitespaces).
• Each line is preceded by 4N space characters, where N is called indentation level.
• The first and the last lines of the program have zero indentation level.
• Lines that constitute block body and are enclosed in curly braces '{'…'}' have one more indentation level.
• No whitespace is allowed inside the line with the exception of the following two cases where a single space character is mandatory: before opening curly brace character '{' and after comma ','.
• Lines (with the only exception of the last line) end with semicolon ';' or opening curly brace '{' characters. These characters cannot appear in the middle or at the beginning of any line (including the last one).
• Closing curly brace '}' characters appear only at the beginning of lines after indentation spaces.

See sample output section for an example of properly formatted trivial program.

Input file format

Output file format

Constraints

Sample tests

{class(Point) 
{
 member ( int ( x ) ) ; member ( int ( y ) ) ;
 member ( fun ( Length )  
 {
   return ( sqrt ( sum ( sqr ( x ),sqr ( y ) ) ) );
 } ) ;
};
Main 
{
 repeat 
 {
   set ( n,input ( int ) ) ;
   for ( int ( i,0 ) , lt ( i,n ) , inc ( i ) ) 
   {
     print ( mult ( n,n ) ) ;
   };
 };
}; }

{
    class(Point) {
        member(int(x));
        member(int(y));
        member(fun(Length) {
            return(sqrt(sum(sqr(x), sqr(y))));
        });
    };
    Main {
        repeat {
            set(n, input(int));
            for(int(i, 0), lt(i, n), inc(i)) {
                print(mult(n, n));
            };
        };
    };
}
  

Problem F. Farmer Bill's Problem ≡

Statement

It is rumored that the planet Earth is often visited by Unidentified Flying Objects (UFOs). Sometimes UFOs land and leave burned out regions. Observations show that these regions have the form of circles.

Recently farmer Bill has found such circles on his nice rectangular wheat field. Bill likes all mysterious things very much, so he has decided to keep these circles on the field. However, although being an ufolog, first of all Bill is the farmer, so he needs to harvest his wheat. Therefore he has decided to keep some regions containing circles intact, and harvest the rest of the field.

All regions that Bill keeps unharvested must be rectangles that neither touch nor overlap each other. The sides of the rectangles must be parallel to the sides of the field. All circles left by UFOs must be inside these regions. The total area of the regions must be minimal possible, so that Bill could harvest the maximal possible part of his field.

Now Bill wants to know the total area of the field that he will be able to harvest. Help him!

Input file format

The first line of the input file contains two integer numbers x and y  — the dimensions of Bill's field. Let Bill's field be positioned on the plane in such a way that its corners are located in points with coordinates (0, 0), (x, 0), (x, y) and (0, y).

The second line of the input file contains N — the number of circles left by UFOs on Bill's field. Next N lines describe circles: each line contains three positive integer numbers x_i, y_i and r_i — coordinates of the center and radius of the circle. Circles may touch, overlap or contain each other. All circles are completely located within the field bounds.

Output file format

Constraints

Sample tests

10 8
2
4 4 2
6 4 1

60

10 8
2
3 3 1
1 1 1

64