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Problem 3. Quadratic equation

Problem description

Solving a linear equation is too hard, so we will solve a quadratic equation. A quadratic equation is of the form $ax^2+bx+c=0$, where $a,b,c$ are constant real numbers and the unknown $x\in\mathbb R$.

Given the coefficients $a,b$ and $c$, your task is to solve the quadratic equation $ax^2+bx+c=0$.

To make the problem easier, $a$ may be zero. To make the problem harder, it is guaranteed that $a,b,c\in\mathbb Z$.

Solve the equation and output the solution(s).

• If the equation is a quadratic one, your output should be of one of the following forms (where ??? is replaced with the exact solution):
  • x1 = x2 = ???
  • x1 = ???, x2 = ??? where $x_1<x_2$
  • No solution.
• Otherwise, your output should be of one of the following forms (where ??? is replaced with the exact solution):
  • x = ???
  • No solution.
  • x\in\mathbb{R}, indicating $x\in\mathbb R$ in $\LaTeX$

All the output numbers should be rounded to three decimal places.

It is guaranteed that $|a|,|b|,|c|\leqslant 100$.

The first five testcases are linear equations. The rest are quadratic equations.

Examples

Example 1

Input

1 2 1

Output

x1 = x2 = -1.000

Example 2

Input

1 0 1

Output

No solution.

Example 3

Input

0 0 0

Output

x\in\mathbb{R}

Example 4

Input

1 3 2

Output

x1 = -2.000, x2 = -1.000