CF1399B.Gifts Fixing

You have $n$ gifts and you want to give all of them to children. Of course, you don't want to offend anyone, so all gifts should be equal between each other. The $i$-th gift consists of $a_i$ candies and $b_i$ oranges.

During one move, you can choose some gift $1 \le i \le n$ and do one of the following operations:

• eat exactly one candy from this gift (decrease $a_i$ by one);
• eat exactly one orange from this gift (decrease $b_i$ by one);
• eat exactly one candy and exactly one orange from this gift (decrease both $a_i$ and $b_i$ by one).

Of course, you can not eat a candy or orange if it's not present in the gift (so neither $a_i$ nor $b_i$ can become less than zero).

As said above, all gifts should be equal. This means that after some sequence of moves the following two conditions should be satisfied: $a_1 = a_2 = \dots = a_n$ and $b_1 = b_2 = \dots = b_n$ (and $a_i$ equals $b_i$ is not necessary).

Your task is to find the minimum number of moves required to equalize all the given gifts.

You have to answer $t$ independent test cases.

你有 $n$ 件礼物，希望将它们全部分给孩子们。当然，你不想让任何人感到被冒犯，因此所有礼物之间必须完全相同。第 $i$ 件礼物包含 $a_i$ 颗糖果和 $b_i$ 个橙子。

在一次操作中，你可以选择某一件礼物 $1 \le i \le n$，并执行以下三种操作之一：

• 从该礼物中恰好吃掉一颗糖果（即令 $a_i$ 减少 1）；
• 从该礼物中恰好吃掉一个橙子（即令 $b_i$ 减少 1）；
• 从该礼物中恰好吃掉一颗糖果和一个橙子（即同时令 $a_i$ 和 $b_i$ 各减少 1）。

当然，你不能吃掉不存在的糖果或橙子（即 $a_i$ 和 $b_i$ 均不能变为负数）。

如前所述，所有礼物必须变得完全相同。这意味着经过若干次操作后，需满足如下两个条件：$a_1 = a_2 = \dots = a_n$ 且 $b_1 = b_2 = \dots = b_n$（注意：不要求对任意 $i$ 都有 $a_i = b_i$）。

你的任务是求出使所有给定礼物变得相同的最少操作次数。

你需要回答 $t$ 个相互独立的测试用例。

The first line of the input contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ($1 \le n \le 50$) — the number of gifts. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the number of candies in the $i$-th gift. The third line of the test case contains $n$ integers $b_1, b_2, \dots, b_n$ ($1 \le b_i \le 10^9$), where $b_i$ is the number of oranges in the $i$-th gift.

输入的第一行包含一个整数 $t$（$1 \le t \le 1000$），表示测试用例的数量。接下来是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 50$），表示礼物的数量。
每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$），其中 $a_i$ 表示第 $i$ 个礼物中的糖果数量。
每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$1 \le b_i \le 10^9$），其中 $b_i$ 表示第 $i$ 个礼物中的橘子数量。

For each test case, print one integer: the minimum number of moves required to equalize all the given gifts.

对于每个测试用例，输出一个整数：使所有给定礼物相等所需的最少移动次数。

In the first test case of the example, we can perform the following sequence of moves:

• choose the first gift and eat one orange from it, so $a = [3, 5, 6]$ and $b = [2, 2, 3]$;
• choose the second gift and eat one candy from it, so $a = [3, 4, 6]$ and $b = [2, 2, 3]$;
• choose the second gift and eat one candy from it, so $a = [3, 3, 6]$ and $b = [2, 2, 3]$;
• choose the third gift and eat one candy and one orange from it, so $a = [3, 3, 5]$ and $b = [2, 2, 2]$;
• choose the third gift and eat one candy from it, so $a = [3, 3, 4]$ and $b = [2, 2, 2]$;
• choose the third gift and eat one candy from it, so $a = [3, 3, 3]$ and $b = [2, 2, 2]$.

在示例的第一个测试用例中，我们可以执行以下操作序列：

• 选择第一个礼物并从中吃掉一个橘子，此时 $a = [3, 5, 6]$，$b = [2, 2, 3]$；
• 选择第二个礼物并从中吃掉一颗糖果，此时 $a = [3, 4, 6]$，$b = [2, 2, 3]$；
• 选择第二个礼物并从中吃掉一颗糖果，此时 $a = [3, 3, 6]$，$b = [2, 2, 3]$；
• 选择第三个礼物并从中各吃掉一颗糖果和一个橘子，此时 $a = [3, 3, 5]$，$b = [2, 2, 2]$；
• 选择第三个礼物并从中吃掉一颗糖果，此时 $a = [3, 3, 4]$，$b = [2, 2, 2]$；
• 选择第三个礼物并从中吃掉一颗糖果，此时 $a = [3, 3, 3]$，$b = [2, 2, 2]$。