CF1530C Pursuit

你和你的朋友伊利亚正在参加由多个阶段组成的编程竞赛。 对于每个阶段，你和伊利亚都会获得一个分数，保证为 $0$ 到 $100$ 之间的整数。并且，每个人获得的分数都是相互独立的，不受对方影响。 总分是这样计算的：设当前已进行 $k$ 个阶段，则你的总分为最高的 $k-\left\lfloor k\div4\right\rfloor $个阶段得分之和。其中 $\left\lfloor a\right\rfloor$ 代表 $a$ 向下取整（不大于 $a$ 的最大整数）。 现在，这个竞赛已进行了 $n$ 个阶段，你也知道这些阶段中，两个人获得的分数。但比赛仍在进行。请问：理论上，至少再过多少个阶段，你的总分才能超过伊利亚？如果你的总分已经超过了她，请输出 `0`。

第一行一个整数 $t$（$1\le t\le1000$），代表测试数据组数。 对于每个测试数据，第一行一个整数 $n$（$1\le n\le10^5$），代表已经进行了 $n$ 个阶段。 接下来有两行，每行都有 $n$ 个数。第一行代表你的每个阶段的得分，第二行代表伊利亚每个阶段的得分。

对于每个测试数据，输出一行，一个整数，即问题所求的答案。如果你的总分已经超过了她，请输出 `0`。 Translated by [dengzijun](https://www.luogu.com.cn/user/387836)

In 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.