Equation Solver

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

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

Input

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

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

1997/98 University of Ulm Local Contest