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.

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.

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

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] $ .