Consider an N-degree polynomial, expressed as follows:

P_N * x^N + P_N-1 * x^N-1 + ... + P₁ * x¹ + P₀ * 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 a^b + c * d should be evaluated as a^((b+c)*d). For our purposes, exponentiation is right-associative (in other words, a^bc = 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 ith of these lines contains the integer P_i-1.

Output

For the ith 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 ≤ P_i ≤ 50
P_N ≠ 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.