Solving Linear Equations

You are given linear equations in a single unknown. Write a program that finds the solution of each equation.

The input consists of several equations, one per line.

Every equation is at most 100 characters long and follows the EBNF grammar below.

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

This grammar can also produce non-linear expressions such as x*x = 25, but the input always gives an equation that is linear in x. Moreover, every sub-expression of an equation is also linear, so an expression such as x*x - x*x + x = 0 (where x*x is not linear) is never given.

Every number that appears in the input is a non-negative integer, and x is a real number.

For each test case, first print Equation #i, where i is the test case number (starting from 1). On the next line, print exactly one of the following.

• If the equation has no solution, print No solution.
• If the equation has infinitely many solutions, print Infinitely many solutions.
• If the equation has a unique solution, print x = solution, where solution is printed with six digits after the decimal point.

Print one blank line between consecutive test cases.