Fourth Great and Bountiful Human Empire is developing a transconduit tunnel network connecting all its planets. The Empire consists of planets, represented as points in the 3D space. The cost of forming a transconduit tunnel between planets and is:

where are 3D coordinates of planet , and are coordinates of planet . The Empire needs to build exactly tunnels in order to fully connect all planets, either by direct links or by a chain of links. You need to come up with the lowest possible cost of successfully completing this project.

#### Input Specification

The first line of input contains one integer , number of planets.

The next lines contain exactly integers each. All integers are between and inclusive. Each line contains the , , and coordinate of one planet (in order).

**No two planets will occupy the exact same point in space.**

#### Output Specification

The first and only line of output should contain the minimal cost of forming the network of tunnels.

#### Sample Input 1

```
2
1 5 10
7 8 2
```

#### Sample Output 1

`3`

#### Sample Input 2

```
3
-1 -1 -1
5 5 5
10 10 10
```

#### Sample Output 2

`11`

#### Sample Input 3

```
5
11 -15 -15
14 -5 -15
-1 -1 -5
10 -4 -1
19 -4 19
```

#### Sample Output 3

`4`

## Comments