You are given the polynomial F(x) as the sum of monomials. Each monomial has the form:
[coefficient*]x[^degree] or [coefficient],
where coefficient and degree are integers such that -30000 <= coefficient <= 30000, 0 <= degree <= 6. The parameters given in [] can be skipped.
In this problem you have to find all solutions of the equation: F(x)=0.

Input

t – the number of test cases, then t test cases follow. [t <= 100]
Each line contains one polynomial F(x) given as string s in the form described above.
The length of string s is not more than 300 characters.

Output

For each test case output all solutions (including repeated) of the given equation in non-decreasing order. All solutions lie within the interval [-100.0; 100.0]. Each solution must be given with an error of not more than 0.01. It's guaranteed that all solutions are real, not complex.

Example

Input:
2
x^4-6*x^3+11*x^2-6*x
-x^2+2*x-1

Output:
0.00 1.00 2.00 3.00
1.00 1.00