Zeroes of polynomials P97780

Given a function f continuous in an interval [a,b], and such that f(a) · f(b) < 0, a basic theorem of Mathematics states that there must exist at least one zero of f in (a,b), that is, a real number z such that a < z < b and f(z) = 0.

Given a polynomial p(x) = c₄ x⁴ + c₃ x³ + c₂ x² + c₁ x + c₀ with exactly one zero in (0,1), can you find this zero?

Input

Each input line describes a polynomial p(x) of degree at most 4 with exactly one zero in ‍(0,1). Each polynomial is given in decreasing order of ‍i as follows: c₄ 4 c₃ 3 c₂ 2 c₁ 1 c₀ 0. Every c_i is a real number. The pairs c_i i with c_i = 0 are not present in the input.

Output

For every polynomial, print its case number, followed by an approximation of its zero z in ‍(0,1), with the following convention: z must be a real number with exactly 5 digits after the decimal point, such that 0 ≤ z ≤ 0.99999 and p(z) · p(z + 0.00001) < 0. Always print the 5 decimal digits of z.

Observations

• Every given polynomial is such that p(x) ≠ 0 for every real number x ∈ [0,1] that has ‍5 (or less) decimal digits after the decimal point.
• The test cases have no precisions issues. However, be aware that it is not wise to check the property p(z) · p(z + 0.00001) < 0 just like this.