Solving a System of Linear Equations

Given an \(n\times n\) system of linear equations:

$$\begin{cases} a_{1,1}x_1+a_{1,2}x_2+\cdots+a_{1,n}x_n=b_1\\ a_{2,1}x_1+a_{2,2}x_2+\cdots+a_{2,n}x_n=b_2\\ \vdots \\ a_{n,1}x_1+a_{n,2}x_2+\cdots+a_{n,n}x_n=b_n \end{cases} $$

Your task is to determine the solution of the system. If there is a unique solution, output the values of \(x_1,x_2,\dots,x_n\) (each formatted to 6 decimal places) separated by a space. If the system has infinitely many solutions, output Infinite solutions. If there is no solution, output No solution.

inputFormat

The first line contains an integer \(n\) representing the number of equations and unknowns. The following \(n\) lines each contain \(n+1\) space-separated numbers. The first \(n\) numbers of each line represent the coefficients \(a_{i,1}, a_{i,2}, \dots, a_{i,n}\) and the last number is the constant \(b_i\).

For example:

3
1 0 0 1
0 1 0 2
0 0 1 3

outputFormat

If the system has a unique solution, output the solution values \(x_1, x_2, \dots, x_n\) in order, each formatted with 6 decimal places and separated by a space. If the system has infinitely many solutions, output Infinite solutions. If there is no solution, output No solution.

sample

3
1 0 0 1
0 1 0 2
0 0 1 3

1.000000 2.000000 3.000000