#20Medium

System of equations

Time: 1 s · Memory: 256 MB

Variables and types

Statement

You are given a system of two linear equations with two unknowns:

$\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$

The system has a unique solution. Find $x$ and $y$ .

Input format

The first line contains $a_1$ , $b_1$ , $c_1$ and the second line contains $a_2$ , $b_2$ , $c_2$ : integers, each at most $100$ in absolute value. $a_1 b_2 - a_2 b_1 \ne 0$ .

Output format

A single line with two numbers: $x$ and $y$ , each with exactly 2 digits after the decimal point.

Examples

Input

1 1 5
2 -1 4

Output

3.00 2.00

Input

2 3 13
1 -1 -1

Output

2.00 3.00

Note

Cramer's rule: $D = a_1 b_2 - a_2 b_1$ , $x = \dfrac{c_1 b_2 - c_2 b_1}{D}$ , $y = \dfrac{a_1 c_2 - a_2 c_1}{D}$ .

In the first example: $D = 1 \cdot (-1) - 2 \cdot 1 = -3$ , $x = \dfrac{5 \cdot (-1) - 4 \cdot 1}{-3} = 3$ , $y = \dfrac{1 \cdot 4 - 2 \cdot 5}{-3} = 2$ .

System of equations

Time: 1 s · Memory: 256 MB

Variables and types

Statement

You are given a system of two linear equations with two unknowns:

$\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$

The system has a unique solution. Find $x$ and $y$ .

Input format

The first line contains $a_1$ , $b_1$ , $c_1$ and the second line contains $a_2$ , $b_2$ , $c_2$ : integers, each at most $100$ in absolute value. $a_1 b_2 - a_2 b_1 \ne 0$ .

Output format

A single line with two numbers: $x$ and $y$ , each with exactly 2 digits after the decimal point.

Examples

Input

1 1 5
2 -1 4

Output

3.00 2.00

Input

2 3 13
1 -1 -1

Output

2.00 3.00

Note

Cramer's rule: $D = a_1 b_2 - a_2 b_1$ , $x = \dfrac{c_1 b_2 - c_2 b_1}{D}$ , $y = \dfrac{a_1 c_2 - a_2 c_1}{D}$ .

In the first example: $D = 1 \cdot (-1) - 2 \cdot 1 = -3$ , $x = \dfrac{5 \cdot (-1) - 4 \cdot 1}{-3} = 3$ , $y = \dfrac{1 \cdot 4 - 2 \cdot 5}{-3} = 2$ .