 The 2019 Nordic Collegiate Programming Contest

#### Start

2019-10-05 01:00 AKDT

## The 2019 Nordic Collegiate Programming Contest

#### End

2019-10-05 06:00 AKDT
The end is near!
Contest is over.
Not yet started.
Contest is starting in -392 days 15:40:31

5:00:00

0:00:00

# Problem BBuilding Boundaries

Maarja wants to buy a rectangular piece of land and then construct three buildings on that land.

The boundaries of the buildings on the ground must have rectangular sizes $a_1 \times b_1$, $a_2 \times b_2$, and $a_3 \times b_3$. They can touch each other but they may not overlap. They can also be rotated as long as their sides are horizontal and vertical.

What is the minimum area of land Maarja has to buy? Figure 1: Illustration of the two test scenarios in Sample Input 1 and their solutions. In the second scenario the $5 \times 1$ building has been rotated by $90$ degrees.

## Input

The input consists of multiple test scenarios. The first line of input contains a single integer $t$ ($1 \le t \le 1000$), the number of scenarios. Then follow the $t$ scenarios. Each scenario consists of a single line, containing six integers $a_1$, $b_1$, $a_2$, $b_2$, $a_3$ and $b_3$ ($1 \le a_1,b_1,a_2,b_2,a_3,b_3 \le 10^9$).

## Output

For each test scenario, output the minimum area of land such that Maarja can construct the three buildings.

Sample Input 1 Sample Output 1
2
2 3 2 2 1 1
2 4 5 1 2 3

12
21