Comets have recently passed through your region of space, leaving behind a trail of dust. You would like to get a rough idea of the extent of this pollution, by finding the two most distant dust particles. Here, we define distance as the sum of differences between the `x`-, `y`-, and `z`-coordinates. For example, the distance between two particles at (1, 4, 9) and (4, 4, 4) is 3 + 0 + 5 = 8.

There are `N` comets, and we describe each comet with 11 numbers: (`A`, `B`, `C`), (`D`, `E`, `F`), (`G`, `H`, `I`), and (`U`, `V`). A comet’s position at time `t` is given by (`A``t`^{2} + `B``t` + `C`, `D``t`^{2} + `E``t` + `F`, `G``t`^{2} + `H``t` + `I`). A comet leaves behind a particle of dust at every integer time `t` between `U` and `V`, inclusive.

For example, consider a comet described by (1, 0, 0), (0, −2, 1), (0, 0, 6), and (1, 5). It leaves behind 5 dust particles, at (1, −1, 6), (4, −3, 6), (9, −5, 6), (16, −7, 6), and (25, −9, 6). The first and last points are the most distant pair, with distance 24 + 8 + 0 = 32.

Pay close attention to the bounds. You may assume that there will be fewer than 100,000 dust particles, and that all positions will fit within a signed 32-bit integer.

- 1 ≤
`N`≤ 100 - −500 ≤
`A`,`D`,`G`,`U`,`V`≤ 500 - −100,000 ≤
`B`,`C`,`E`,`F`,`H`,`I`≤ 100,000 `U`≤`V`

The input file **DATA5.txt** will contain 5 test cases. Each will begin with a single integer `N`. `N` lines will follow, each containing 11 integers, in the order described above.

The output file **OUT5.txt** will contain 5 lines of output, one integer for each test case: the distance between the most distant pair of dust particles. There will be at least 2 dust particles.

```
1
1 0 0 0 -2 1 0 0 6 1 5
3
3 1 4 1 5 9 2 6 5 3 58
2 7 1 8 2 8 1 8 2 8 45
1 6 1 8 0 3 3 9 8 8 74
```

```
32
66726
```