Imagine that you are the owner of a news website and want to study how some selected news items affect your users. You have (n) news items, and for each of them, you have already determined two parameters: how much it touches politics (p_i) and how much it touches culture (c_i). You also have (m) users whose reaction to the news you want to study. For each person, you have already determined three parameters: tolerance to political news (tp_j), tolerance to cultural news (tc_j), and the "zone of influence" (d_j). The influence of politics (I_p(i, j)) and culture (I_c(i, j)) in news item (i) on user (j) can be calculated by the following formulas: In other words, while the amount of politics (p_i) is less than the tolerance level (tp_j), it does not affect the user. Otherwise, the topic starts to irritate the user, but not more than up to (tp_j + d_j). The same goes for culture. The total influence of news item (i) on user (j) is (I(i, j) = I_p(i, j) + I_c(i, j)). For each user (j), determine the minimum influence (I(i, j)) among all news items (i). The first line contains one integer (n) ((1 \le n \le 2 \cdot 10^5)) — the number of news items. The second line contains (n) integers (p_1, p_2, \dots, p_n) ((0 \le p_i \le 10^6)) — the amount of political content of each news item. The third line contains (n) integers (c_1, c_2, \dots, c_n) ((0 \le c_i \le 10^6)) — the amount of cultural content of each news item. The fourth line contains one integer (m) ((1 \le m \le 4 \cdot 10^5)) — the number of users. The fifth line contains (m) integers (tp_1, tp_2, \dots, tp_m) ((0 \le tp_j \le 10^6)) — the political tolerance of each user. The sixth line contains (m) integers (tc_1, tc_2, \dots, tc_m) ((0 \le tc_j \le 10^6)) — the cultural tolerance of each user. The seventh line contains (m) integers $$$d_1, d_2, \dots, d_m