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 Number Digit := Factor { '' Factor } := Number | 'x' | '(' Expression ')' := Digit | Digit Number := '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, but the last one. Sample Input x+x+x=10 4x+2=19 3x=3x+1+2+3 (42-6*7)x=25-10 Sample Output Equation #1 x = 3.333333 Equation #2
2/2 x = 4.250000 Equation #3 No solution. Equation #4 Infinitely many solutions.