Two-finger Programming

Time Limit : 8 sec, Memory Limit : 65536 KB

Problem F: Two-finger Programming

Franklin Jenkins is a programmer, but he isnft good at typing keyboards. So he always uses only eff and ejf (keys on the home positions of index fingers) for variable names. He insists two characters are enough to write programs, but naturally his friends donft agree with him: they say it makes programs too long.

He asked you to show any program can be converted into not so long one with the f-j names. Your task is to answer the shortest length of the program after all variables are renamed into the f-j names, for each given program.

Given programs are written in the language specified below.

A block (a region enclosed by curly braces: e{f and e}f) forms a scope for variables. Each scope can have zero or more scopes inside. The whole program also forms the global scope, which contains all scopes on the top level (i.e., out of any blocks).

Each variable belongs to the innermost scope which includes its declaration, and is valid from the decla- ration to the end of the scope. Variables are never redeclared while they are valid, but may be declared again once they have become invalid. The variables that belong to different scopes are regarded as differ- ent even if they have the same name. Undeclared or other invalid names never appear in expressions.

The tokens are defined by the rules shown below. All whitespace characters (spaces, tabs, linefeeds, and carrige-returns) before, between, and after tokens are ignored.

token:
     identifier | keyword | number | operator | punctuation
identifier:
     [a-z]+ (one or more lowercase letters)
keyword:
     [A-Z]+ (one or more uppercase letters)
number:
     [0-9]+ (one or more digits)
operator:
     e=f | e+f | e-f | e*f | e/f | e&f | e|f | e^f | ef
punctuation:
     e{f | e}f | e(f | e)f | e;f

The syntax of the language is defined as follows.

program:
     statement-list
statement-list:
     statement
     statement-list statement
statement:
     variable-declaration
     if-statement
     while-statement
     expression-statement
     block-statement
variable-declaration:
      gVARh identifier e;f
if-statement:
      gIFh e(f expression e)f block-statement
while-statement:
      gWHILEh e(f expression e)f block-statement
expression-statement:
      expression e;f
block-statement:
      e{f statement-listoptional e}f
expression:
      identifier
      number
      expression operator expression

Input

The input consists of multiple data sets.

Each data set gives a well-formed program according to the specification above. The first line contains a positive integer N, which indicates the number of lines in the program. The following N lines contain the program body.

There are no extra characters between two adjacent data sets.

A single line containing a zero indicates the end of the input, and you must not process this line as part of any data set.

Each line contains up to 255 characters, and all variable names are equal to or less than 16 characters long. No program contains more than 1000 variables nor 100 scopes (including the global scope).

Output

For each data set, output in one line the minimum program length after all the variables are renamed into the f-j name. Whitespace characters must not counted for the program length. You are not allowed to perform any operations on the programs other than renaming the variables.

Sample Input

14
VAR ga;
VAR gb;
IF(ga > gb) {
  VAR saa;
  VAR sab;
  IF(saa > ga) {
    saa = sab;
  }
}
WHILE(gb > ga) {
  VAR sba;
  sba = ga;
  ga = gb;
}
7
VAR thisisthelongest;
IF(thisisthelongest / 0) {
  VARone;
  one = thisisthelongest + 1234567890123456789012345;
}
VAR another;
32 = another;
0

Output for the Sample Input

73
59


The two programs should be translated as follows:

VAR f;
VAR ff;
IF(f > ff) {
  VAR j;
  VAR fj;
  IF(j > f) {
    j = fj;
  }
}
WHILE(ff > f) {
  VAR j;
  j = f;
  f = ff;
}
VAR j;
IF(j / 0) {
  VARf;
  f = j + 1234567890123456789012345;
}
VAR f;
32 = f;

Source: ACM-ICPC Japan Alumni Group Summer Camp 2007 , Day 3, Tokyo, Japan, 2007-09-24
http://acm-icpc.aitea.net/