C. Pursuittime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou and your friend Ilya are participating in an individual programming contest consisting of multiple stages. A contestant can get between 0 and 100 points, inclusive, for each stage, independently of other contestants.Points received by contestants in different stages are used for forming overall contest results. Suppose that k stages of the contest are completed. For each contestant, k - \lfloor \frac{k}{4} \rfloor stages with the highest scores are selected, and these scores are added up. This sum is the overall result of the contestant. (Here \lfloor t \rfloor denotes rounding t down.)For example, suppose 9 stages are completed, and your scores are 50, 30, 50, 50, 100, 10, 30, 100, 50. First, 7 stages with the highest scores are chosen — for example, all stages except for the 2-nd and the 6-th can be chosen. Then your overall result is equal to 50 + 50 + 50 + 100 + 30 + 100 + 50 = 430.As of now, n stages are completed, and you know the points you and Ilya got for these stages. However, it is unknown how many more stages will be held. You wonder what the smallest number of additional stages is, after which your result might become greater than or equal to Ilya's result, at least in theory. Find this number!InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 1000). Description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 10^5) — the number of completed stages.The second line contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le 100) — your points for the completed stages.The third line contains n integers b_1, b_2, \ldots, b_n (0 \le b_i \le 100) — Ilya's points for the completed stages.It is guaranteed that the sum of n over all test cases does not exceed 10^5.OutputFor each test case print a single integer — the smallest number of additional stages required for your result to be able to become greater than or equal to Ilya's result.If your result is already not less than Ilya's result, print 0.ExampleInput
5
1
100
0
1
0
100
4
20 30 40 50
100 100 100 100
4
10 20 30 40
100 100 100 100
7
7 59 62 52 27 31 55
33 35 50 98 83 80 64
Output
0
1
3
4
2
NoteIn the first test case, you have scored 100 points for the first stage, while Ilya has scored 0. Thus, your overall result (100) is already not less than Ilya's result (0).In the second test case, you have scored 0 points for the first stage, while Ilya has scored 100. A single stage with an opposite result is enough for both your and Ilya's overall scores to become equal to 100.In the third test case, your overall result is 30 + 40 + 50 = 120, while Ilya's result is 100 + 100 + 100 = 300. After three additional stages your result might become equal to 420, while Ilya's result might become equal to 400.In the fourth test case, your overall result after four additional stages might become equal to 470, while Ilya's result might become equal to 400. Three stages are not enough.
5
1
100
0
1
0
100
4
20 30 40 50
100 100 100 100
4
10 20 30 40
100 100 100 100
7
7 59 62 52 27 31 55
33 35 50 98 83 80 64

0 1 3 4 2 
['binary search', 'brute force', 'greedy', 'sortings', '*1200']