Solving a System of Linear Equations

Problem Description

You are given a system of linear equations with $n$ equations and $n$ unknowns. You need to find the value of each unknown.

If the system has no solution, output $-1$; if the system has infinitely many solutions, output $-2$.

The format of the system is as follows (in this problem $m = n$):

Input Format

The first line contains a number $n$, the number of unknowns and equations.

The next $n$ lines each contain $n+1$ numbers; on the $i$-th line, the $j$-th ($1\leq j\leq n$) number is the coefficient $a_{i,j}$, and the $(n+1)$-th number is $b_i$.

Output Format

If a normal solution exists, output $n$ lines each with one number representing the answer. As long as your answer and the standard answer have a relative or absolute error within $10^{-6}$, it is accepted.

If not, output one line with $-1$ or $-2$, see the problem statement for details.

Sample Input 1

2
1.0 2.0 4.0
2.0 1.0 5.0

Sample Output 1

2.0000000000
1.0000000000

Sample Input 2

2
1.0 2.0 4.0
2.0 4.0 5.0

Sample Output 2

-1

Constraints

For $100\%$ of the data, $2\leq n\leq 100, 1\leq i, j\leq n, -10^8\leq a_{i,j}, b_i\leq 10^8$.