310914: CF1909C. Heavy Intervals

C. Heavy Intervalstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputShiki - Pure Ruby⠀

You have $n$ intervals $[l_1, r_1], [l_2, r_2], \dots, [l_n, r_n]$, 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 $c_i \cdot (r_i - l_i)$.

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

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

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

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

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

It is guaranteed that $\{l_1, l_2, \dots, l_n, r_1, r_2, \dots, r_n\}$ are all distinct.

The fourth line of each test case contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le 10^7$) — 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

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

ExampleInput

2
2
8 3
12 23
100 100
4
20 1 2 5
30 4 3 10
2 3 2 3

Output

2400
42

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 $100 \cdot (23-8) = 1500$ in total;
• interval $[3, 12]$ with weight $100$ per unit length, and $100 \cdot (12-3) = 900$ 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 $3 \cdot (3-1) = 6$ in total;
• interval $[2, 4]$ with weight $3$ per unit length, and $3 \cdot (4-2) = 6$ in total;
• interval $[5, 10]$ with weight $2$ per unit length, and $2 \cdot (10-5) = 10$ in total;
• interval $[20, 30]$ with weight $2$ per unit length, and $2 \cdot (30-20) = 20$ 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 $42$.

题目大意：给定n个区间\[l_1, r_1], [l_2, r_2], \dots, [l_n, r_n]\]，每个区间的权重为\[c_i \cdot (r_i - l_i)\]。你可以对区间左端点、右端点和权重进行任意排列，但需保证排列后的区间仍合法（即对于每个区间，左端点小于右端点）。求排列后所有区间权重的最小可能和。

输入数据格式：第一行包含一个整数t，表示测试用例数量。接下来每个测试用例包含4行，第一行包含一个整数n，表示区间数量；第二行包含n个整数，表示每个区间的左端点；第三行包含n个整数，表示每个区间的右端点；第四行包含n个整数，表示每个区间的权重。

输出数据格式：对于每个测试用例，输出一个整数，表示排列后所有区间权重的最小可能和。题目大意：给定n个区间\[l_1, r_1], [l_2, r_2], \dots, [l_n, r_n]\]，每个区间的权重为\[c_i \cdot (r_i - l_i)\]。你可以对区间左端点、右端点和权重进行任意排列，但需保证排列后的区间仍合法（即对于每个区间，左端点小于右端点）。求排列后所有区间权重的最小可能和。 输入数据格式：第一行包含一个整数t，表示测试用例数量。接下来每个测试用例包含4行，第一行包含一个整数n，表示区间数量；第二行包含n个整数，表示每个区间的左端点；第三行包含n个整数，表示每个区间的右端点；第四行包含n个整数，表示每个区间的权重。 输出数据格式：对于每个测试用例，输出一个整数，表示排列后所有区间权重的最小可能和。