Description

We began to learn mathematics since we were young. Presumably, solving equation set is no longer a problem for you, but will you use computers to solve equations? For example, the following equation set.

2x + 5y = 12

4x + 7y = 15

The sample input is a reflection of the equation set and the output is the answer to the equation set.

Format

Input

There are multiple test cases.For each case, first line of the input contains one integer n (1< n <10), which means that there are n equations, one equation row, each row has n+1 numbers, the numbers are all 32-bit integers, the first n numbers are coefficients of equation, and the last number is a constant of equation, and the input numbers are all non-zero.

Output

For each test case, Output solutions, each number retains three decimal places, there are a space between each two numbers, and to ensure that there is no unsolution or multiple solutions.

Samples

2
2 5 12
4 7 15
2
3 2 2
1 4 4

-1.500 3.000
0.000 1.000

Hint