1997/98 ACM International Collegiate Programming Contest
University of Ulm Local Contest

# Problem E

# Equation Solver

Source file: equation.(c|C|pas)
Input file: equation.in

Write a program that can solve linear equations with one variable.

### Input Specification

The input file will contain a number of equations, each one on a separate line. All equations are strings of less than 100 characters which strictly adhere to the following grammar (given in EBNF):

>     Equation   := Expression '=' Expression
>     Expression := Term { ('+' | '-') Term }
>     Term       := Factor { '*' Factor }
>     Factor     := Number | 'x' | '(' Expression ')'
>     Number     := Digit | Digit Number
>     Digit      := '0' | '1' | ... | '9'

Although the grammar would allow to construct non-linear equations like "x*x=25", we guarantee that all equations occuring in the input file will be linear in x. We further guarantee that all sub-expressions of an equation will be linear in x too. That means, there won't be test cases like x*x-x*x+x=0 which is a linear equation but contains non-linear sub-expressions (x*x).
Note that all numbers occuring in the input are non-negative integers, while the solution for x is a real number.

### Output Specification

For each test case, print a line saying "Equation #i (where i is the number of the test case) and a line with one of the following answers:

- If the equation has no solution, print "No solution.".
- If the equation has infinitely many solutions, print "Infinitely many solutions.".
- If the equation has exactly one solution, print "x = solution" where solution is replaced by the appropriate real number (printed to six decimals).

Print a blank line after each test case.

### Sample Input

    x+x+x=10
    4*x+2=19
    3*x=3*x+1+2+3
    (42-6*7)*x=2*5-10

### Sample Output

    Equation #1
    x = 3.333333

    Equation #2
    x = 4.250000

    Equation #3
    No solution.

    Equation #4
    Infinitely many solutions.