Equation Solver

Time Limit: 2 Seconds
Memory Limit: 65536 KB

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

**Input**

The input 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**

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.

Source:

**University of Ulm Local Contest 1997**
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