CF1119D Frets On Fire

Miyako came to the flea kingdom with a ukulele. She became good friends with local flea residents and played beautiful music for them every day. In return, the fleas made a bigger ukulele for her: it has $ n $ strings, and each string has $ (10^{18} + 1) $ frets numerated from $ 0 $ to $ 10^{18} $ . The fleas use the array $ s_1, s_2, \ldots, s_n $ to describe the ukulele's tuning, that is, the pitch of the $ j $ -th fret on the $ i $ -th string is the integer $ s_i + j $ . Miyako is about to leave the kingdom, but the fleas hope that Miyako will answer some last questions for them. Each question is in the form of: "How many different pitches are there, if we consider frets between $ l $ and $ r $ (inclusive) on all strings?" Miyako is about to visit the cricket kingdom and has no time to answer all the questions. Please help her with this task! Formally, you are given a matrix with $ n $ rows and $ (10^{18}+1) $ columns, where the cell in the $ i $ -th row and $ j $ -th column ( $ 0 \le j \le 10^{18} $ ) contains the integer $ s_i + j $ . You are to answer $ q $ queries, in the $ k $ -th query you have to answer the number of distinct integers in the matrix from the $ l_k $ -th to the $ r_k $ -th columns, inclusive.

The first line contains an integer $ n $ ( $ 1 \leq n \leq 100\,000 $ ) — the number of strings. The second line contains $ n $ integers $ s_1, s_2, \ldots, s_n $ ( $ 0 \leq s_i \leq 10^{18} $ ) — the tuning of the ukulele. The third line contains an integer $ q $ ( $ 1 \leq q \leq 100\,000 $ ) — the number of questions. The $ k $ -th among the following $ q $ lines contains two integers $ l_k $ ， $ r_k $ ( $ 0 \leq l_k \leq r_k \leq 10^{18} $ ) — a question from the fleas.

Output one number for each question, separated by spaces — the number of different pitches.

For the first example, the pitches on the $66$ strings are as follows. $$\begin{matrix} \textbf{Fret} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} & \textbf{4} & \textbf{5} & \textbf{6} & \textbf{7} & \ldots \\ s_1: & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & \dots \\ s_2: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & \dots \\ s_3: & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & \dots \\ s_4: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & \dots \\ s_5: & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \dots \\ s_6: & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & \dots \end{matrix}$$ There are $5$ different pitches on fret $7$ — $8, 10, 11, 12, 16$ There are $10$ different pitches on frets $0, 1, 2$ — $1, 2, 3, 4, 5, 6, 7, 9, 10, 11$