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 ≤ i ≤ 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 = ... = a_n and b_1 = b_2 = ... = 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.

Input

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

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

Output

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

Example

Input

5 3 3 5 6 3 2 3 5 1 2 3 4 5 5 4 3 2 1 3 1 1 1 2 2 2 6 1 1000000000 1000000000 1000000000 1000000000 1000000000 1 1 1 1 1 1 3 10 12 8 7 5 4

Output

6 16 0 4999999995 7

Note

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].

inputFormat

Input

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

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

outputFormat

Output

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

Example

Input

5 3 3 5 6 3 2 3 5 1 2 3 4 5 5 4 3 2 1 3 1 1 1 2 2 2 6 1 1000000000 1000000000 1000000000 1000000000 1000000000 1 1 1 1 1 1 3 10 12 8 7 5 4

Output

6 16 0 4999999995 7

Note

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].

样例

5
3
3 5 6
3 2 3
5
1 2 3 4 5
5 4 3 2 1
3
1 1 1
2 2 2
6
1 1000000000 1000000000 1000000000 1000000000 1000000000
1 1 1 1 1 1
3
10 12 8
7 5 4

6
16
0
4999999995
7

</p>