write a go solution for Description:
You have n intervals [l_1,r_1],[l_2,r_2],...,[l_n,r_n], such that l_i<r_i for each i, and all the endpoints of the intervals are distinct.

The i-th interval has weight c_i per unit length. Therefore, the weight of the i-th interval is c_i*(r_i-l_i).

You don't like large weights, so you want to make the sum of weights of the intervals as small as possible. It turns out you can perform all the following three operations:

- rearrange the elements in the array l in any order;
- rearrange the elements in the array r in any order;
- rearrange the elements in the array c in any order.

However, after performing all of the operations, the intervals must still be valid (i.e., for each i, l_i<r_i must hold).

What's the minimum possible sum of weights of the intervals after performing the operations?

Input Format:
Each test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows.

The first line of each test case contains a single integer n (1<=n<=10^5) — the number of intervals.

The second line of each test case contains n integers l_1,l_2,ldots,l_n (1<=l_i<=2*10^5) — the left endpoints of the initial intervals.

The third line of each test case contains n integers r_1,r_2,ldots,r_n (l_i<r_i<=2*10^5) — the right endpoints of the initial intervals.

It is guaranteed that l_1,l_2,...,l_n,r_1,r_2,...,r_n are all distinct.

The fourth line of each test case contains n integers c_1,c_2,ldots,c_n (1<=c_i<=10^7) — the initial weights of the intervals per unit length.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output Format:
For each test case, output a single integer: the minimum possible sum of weights of the intervals after your operations.

Note:
In the first test case, you can make

- l=[8,3];
- r=[23,12];
- c=[100,100].

In that case, there are two intervals:

- interval [8,23] with weight 100 per unit length, and 100*(23-8)=1500 in total;
- interval [3,12] with weight 100 per unit length, and 100*(12-3)=900 in total.

The sum of the weights is 2400. It can be shown that there is no configuration of final intervals whose sum of weights is less than 2400.

In the second test case, you can make

- l=[1,2,5,20];
- r=[3,4,10,30];
- c=[3,3,2,2].

In that case, there are four intervals:

- interval [1,3] with weight 3 per unit length, and 3*(3-1)=6 in total;
- interval [2,4] with weight 3 per unit length, and 3*(4-2)=6 in total;
- interval [5,10] with weight 2 per unit length, and 2*(10-5)=10 in total;
- interval [20,30] with weight 2 per unit length, and 2*(30-20)=20 in total.

The sum of the weights is 42. It can be shown that there is no configuration of final intervals whose sum of weights is less than 42.. Output only the code with no comments, explanation, or additional text.