Quaternion Multiplication

An extension of a complex number is called a quaternion. It is a convenient number that can be used to control the arm of a robot because it is convenient for expressing the rotation of an object. Quaternions are $using four real numbers$ x $,$ y $,$ z $,$ w $and special numbers (extended imaginary numbers)$ i $,$ j $,$ k $. It is expressed as x + yi + zj + wk$. The sum of such quaternions is defined as:

$ (x_1 + y_1 i + z_1 j + w_1 k) + (x_2 + y_2 i + z_2 j + w_2 k) = (x_1 + x_2) + (y_1 + y_2) i + (z_1 + z_2) j + (w_1 + w_2) k $

On the other hand, the product between 1, $i$, $j$, and $k$ is given as follows.

This table represents the product $AB$ of two special numbers $A$ and $B$. For example, the product $ij$ of $i$ and $j$ is $k$, and the product $ji$ of $j$ and $i$ is $-k$.

The product of common quaternions is calculated to satisfy this relationship. For example, the product of two quaternions, $1 + 2i + 3j + 4k$ and $7 + 6i + 7j + 8k$, is calculated as follows:

$(1 + 2i + 3j + 4k) \ times (7 + 6i + 7j + 8k) =$ $7 + 6i + 7j + 8k$ $+ 14i + 12i ^ 2 + 14ij + 16ik$ $+ 21j + 18ji + 21j ^ 2 + 24jk$ $+ 28k + 24ki + 28kj + 32k ^ 2$

By applying the table above

$= -58 + 16i + 36j + 32k$

It will be.

Two quaternions ($x_1 + y_1 i + z_1 j + w_1 k$) and ($) where the four coefficients$ x $,$ y $,$ z $,$ w $ are integers and not all zeros x_2 + y_2 i + z_2 j + w_2 k $), and the product is ($x_3 + y_3 i + z_3 j + w_3 k$), $x_3$, $y_3$, $z_3$, $Create a program that outputs w_3$.

input

Given multiple datasets. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:

$n$ $data_1$ $data_2$ :: $data_n$

The first line gives the number of pairs of quaternions to process $n$ ($n \ leq 10$). The following $n$ line is given the $i$ th quaternion pair of information $data_i$ in the following format:

$x_1$ $y_1$ $z_1$ $w_1$ $x_2$ $y_2$ $z_2$ $w_2$

All coefficients given should be -1000 or more and 1000 or less. The number of datasets does not exceed 50.

output

Prints the product of a given set of quaternions for each dataset.

Example

Input

2 1 2 3 4 7 6 7 8 5 6 7 8 3 2 3 4 0

Output

-58 16 36 32 -50 32 28 48

inputFormat

outputFormat

outputs w_3 $.

input

Given multiple datasets. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:

$n$ $data_1$ $data_2$ :: $data_n$

The first line gives the number of pairs of quaternions to process $n$ ($n \ leq 10$). The following $n$ line is given the $i$ th quaternion pair of information $data_i$ in the following format:

$x_1$ $y_1$ $z_1$ $w_1$ $x_2$ $y_2$ $z_2$ $w_2$

All coefficients given should be -1000 or more and 1000 or less. The number of datasets does not exceed 50.

output

Prints the product of a given set of quaternions for each dataset.

Example

Input

2 1 2 3 4 7 6 7 8 5 6 7 8 3 2 3 4 0

Output

-58 16 36 32 -50 32 28 48

样例

2
1 2 3 4 7 6 7 8
5 6 7 8 3 2 3 4
0

-58 16 36 32
-50 32 28 48

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