CF1437C.Chef Monocarp

Chef Monocarp has just put $n$ dishes into an oven. He knows that the $i$-th dish has its optimal cooking time equal to $t_i$ minutes.

At any positive integer minute $T$ Monocarp can put no more than one dish out of the oven. If the $i$-th dish is put out at some minute $T$, then its unpleasant value is $|T - t_i|$ — the absolute difference between $T$ and $t_i$. Once the dish is out of the oven, it can't go back in.

Monocarp should put all the dishes out of the oven. What is the minimum total unpleasant value Monocarp can obtain?

厨师 Monocarp 刚刚将 $n$ 道菜放入烤箱中。他已知第 $i$ 道菜的最佳烹饪时间为 $t_i$ 分钟。

在任意正整数分钟 $T$，Monocarp 最多只能从烤箱中取出一道菜。若第 $i$ 道菜在某一分钟 $T$ 被取出，则其不适值（unpleasant value）为 $|T - t_i|$ —— 即 $T$ 与 $t_i$ 的绝对差值。一旦某道菜被取出烤箱，便不可再放回。

Monocarp 必须将所有菜肴都从烤箱中取出。Monocarp 能获得的最小总不适值是多少？

The first line contains a single integer $q$ ($1 \le q \le 200$) — the number of testcases.

Then $q$ testcases follow.

The first line of the testcase contains a single integer $n$ ($1 \le n \le 200$) — the number of dishes in the oven.

The second line of the testcase contains $n$ integers $t_1, t_2, \dots, t_n$ ($1 \le t_i \le n$) — the optimal cooking time for each dish.

The sum of $n$ over all $q$ testcases doesn't exceed $200$.

第一行包含一个整数 $q$（$1 \le q \le 200$）——测试用例的数量。

接下来是 $q$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 200$）——烤箱中菜肴的数量。

每个测试用例的第二行包含 $n$ 个整数 $t_1, t_2, \dots, t_n$（$1 \le t_i \le n$）——每道菜肴的最佳烹饪时间。

所有 $q$ 个测试用例的 $n$ 值之和不超过 $200$。

Print a single integer for each testcase — the minimum total unpleasant value Monocarp can obtain when he puts out all the dishes out of the oven. Remember that Monocarp can only put the dishes out at positive integer minutes and no more than one dish at any minute.

对每个测试用例，输出一个整数——Monocarp 将所有菜肴从烤箱中取出时所能得到的最小总不愉快值。注意：Monocarp 只能在正整数分钟时刻取出菜肴，且任意一分钟最多只能取出一道菜。

In the first example Monocarp can put out the dishes at minutes $3, 1, 5, 4, 6, 2$. That way the total unpleasant value will be $|4 - 3| + |2 - 1| + |4 - 5| + |4 - 4| + |6 - 5| + |2 - 2| = 4$.

In the second example Monocarp can put out the dishes at minutes $4, 5, 6, 7, 8, 9, 10$.

In the third example Monocarp can put out the dish at minute $1$.

In the fourth example Monocarp can put out the dishes at minutes $5, 1, 2, 4, 3$.

In the fifth example Monocarp can put out the dishes at minutes $1, 3, 4, 5$.

在第一个例子中，Monocarp 可以在第 $3, 1, 5, 4, 6, 2$ 分钟端出菜肴。此时总不适值为 $|4 - 3| + |2 - 1| + |4 - 5| + |4 - 4| + |6 - 5| + |2 - 2| = 4$。

在第二个例子中，Monocarp 可以在第 $4, 5, 6, 7, 8, 9, 10$ 分钟端出菜肴。

在第三个例子中，Monocarp 可以在第 $1$ 分钟端出菜肴。

在第四个例子中，Monocarp 可以在第 $5, 1, 2, 4, 3$ 分钟端出菜肴。

在第五个例子中，Monocarp 可以在第 $1, 3, 4, 5$ 分钟端出菜肴。