Equation Solver

Time Limit: 1000MS Memory Limit: 65536KB

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.

Example Input

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

Example Output

Equation #1
x = 3.333333

Equation #2
x = 4.250000

Equation #3
No solution.

Equation #4
Infinitely many solutions.

Hint


Author