Chef Monocarp

有$n$到菜品被放入了一个烤炉中，每到菜品都有一个最佳取出的时间$t_i$。现在按照一定顺序把菜品从烤炉中取出，每到菜品都有可能因为不在最佳时间被取出而造成不美味，定义这个不美味度为$|T-t_i|$，其中$T$是取出的时刻。求把所有菜品都取出来的最小不美味度。

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?

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 $ .

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.

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

4
12
0
0
2
21

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 $ .