P2455 [SDOI2006] System of Linear Equations

Given an $n$-variable linear system of equations: $$ \begin{cases} a_{1, 1} x_1 + a_{1, 2} x_2 + \cdots + a_{1, n} x_n = b_1 \\ a_{2, 1} x_1 + a_{2, 2} x_2 + \cdots + a_{2, n} x_n = b_2 \\ \cdots \\ a_{n,1} x_1 + a_{n, 2} x_2 + \cdots + a_{n, n} x_n = b_n \end{cases}$$ Based on the input, write a program to output the status of the solution set.

The first line contains the number of unknowns $n$. Then $n$ lines follow, each containing $n + 1$ integers, representing the coefficients of each equation and the value on the right-hand side.

If there is a unique solution, output the solution. Your result is considered correct if and only if, for every $x_i$, the absolute error or the relative error compared to the standard answer does not exceed $0.01$. If the system has no solution, output $-1$; if it has infinitely many real solutions, output $0$.

Constraints For $100\%$ of the testdata, $1 \le n \le 50$. For all $1 \le i, j \le n$, $\left| a_{i, j} \right| \le 100$, $\left| b_i \right| \le 300$. Translated by ChatGPT 5