# Equation Solver

1000ms 65536K

0 0

Difficult

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

which is a linear equation but contains non-linear sub-expressions (

x*x-x*x+x=0

*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, but the last one.

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

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