The system of linear equations#1076
Professor V. Pucher decided to hold a quiz on linear algebra among first-year students of Baylor University. As one of the assignments, he gave a task to solve a system of linear equations.
While preparing the assignments, the professor encountered the problem of composing various systems of equations for a sufficiently large number of students. As a result, he asked his graduate students to write a coefficient generator. They completed this task and wrote a program that creates linear equations with unknowns. They also provided a program to solve these systems. However, Professor Pucher doubted the answers produced by this program and asked you to develop another that produces correct answers.
Help the professor, and he will help you. :)
The first line of the input file contains the number (0 < N < 7). The next lines (each not longer than characters) contain descriptions of the equations. The equations may contain variable names (x_1, x_2, x_3, x_4, x_5, x_6), not very large integers, and arithmetic operators (, , , ). They may be separated by spaces. Each equation necessarily contains an equality sign ().
If the given system has a unique solution, output the phrase "1 solution.", then in each line (in lexicographic order, without spaces) print the value assigned to each variable as an ordinary irreducible fraction: numerator and denominator separated by a "/". If the answer is an integer, print only the numerator. If there are infinitely many solutions, output the phrase "Infinite solutions.". If the system has no solutions, output "No solution.". It is guaranteed that all numbers in the answer do not exceed one billion.
Example 1