Chef Monocarp

Description:

Input:

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 $$$200$$$.

Output:

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.

Sample Input:

6
6
4 2 4 4 5 2
7
7 7 7 7 7 7 7
1
1
5
5 1 2 4 3
4
1 4 4 4
21
21 8 1 4 1 5 21 1 8 21 11 21 11 3 12 8 19 15 9 11 13

Sample Output:

4
12
0
0
2
21

Note:

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 $$$1, 3, 4, 5$$$.