| Consider an N-degree polynomial, expressed as follows: | |
| **P**N * xN \+ **P**N-1 * xN-1 \+ ... + **P**1 * x1 \+ **P**0 * x0 | |
| You'd like to find all of the polynomial's x-intercepts — in other words, all | |
| distinct real values of x for which the expression evaluates to 0. | |
| Unfortunately, the order of operations has been reversed: Addition (**+**) now | |
| has the highest precedence, followed by multiplication (*****), followed by | |
| exponentiation (**^**). In other words, an expression like ab \+ c * d should | |
| be evaluated as a((b+c)*d). For our purposes, exponentiation is right- | |
| associative (in other words, abc = a(bc)), and 00 = 1. The unary negation | |
| operator still has the highest precedence, so the expression -2-3 * -1 + -2 | |
| evaluates to -2(-3 * (-1 + -2)) = -29 = -512. | |
| ### Input | |
| Input begins with an integer **T**, the number of polynomials. For each | |
| polynomial, there is first a line containing the integer **N**, the degree of | |
| the polynomial. Then, **N**+1 lines follow. The _i_th of these lines contains | |
| the integer **Pi-1**. | |
| ### Output | |
| For the _i_th polynomial, print a line containing "Case #_i_: **K**", where | |
| **K** is the number of distinct real values of **x** for which the polynomial | |
| evaluates to 0. Then print **K** lines, each containing such a value of **x**, | |
| in increasing order. | |
| Absolute and relative errors of up to 10-6 will be ignored in the x-intercepts | |
| you output. However, **K** must be exactly correct. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 200 | |
| 0 ≤ **N** ≤ 50 | |
| -50 ≤ **Pi** ≤ 50 | |
| **PN** ≠ 0 | |
| ### Explanation of Sample | |
| In the first case, the polynomial is 1 * x1 \+ 1 * x0. With the order of | |
| operations reversed, this is evaluated as (1 * x)(((1 + 1) * x)0), which is | |
| equal to 0 only when x = 0. | |
| In the second case, the polynomial does not evaluate to 0 for any real value | |
| x. | |