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문제

1번부터 $N$번까지의 번호가 붙어있는 $N$개의 안테나가 일렬로 놓여 있다. 각 안테나는 다른 연속된 안테나와 1km 떨어져 있다. $i$번 ($1 \le i \le N$) 안테나의 높이는 $H_i$이다. $i$번 안테나는 자신으로 부터 $A_i$km 이상 $B_i$km 이하 떨어져 있는 안테나에게만 정보를 보낼 수 있다. 만약 $x$번 안테나와 $y$번 안테나가 ($1 \le x < y \le N$) 서로 정보를 주고 받을 수 있다면, 이 둘은 통신할 수 있고, 통신 비용은 $|H_x - H_y|$이다.

JOI 공화국의 수상 K씨는 시민들로부터 연결상태에 관한 불만 $Q$개를 들었다. 조사 결과 $j$ 번째 ($1 \le j \le Q$) 불만은, $L_j, \ L_j +1, \cdots, R_j$번 안테나 중 무언가가 이상이 있는것으로 밝혀졌다. 당신은, 이 안테나들중 서로 통신할 수 있는 안테나 쌍이 있는지, 만약 있다면 그 중 가장 통신 비용이 높은 쌍의 통신 비용은 얼마인지 알아보는 일을 맡았다.

안테나의 정보와 불만의 정보가 주어졌을 때, $L_j, \ L_j +1, \cdots, R_j$번 안테나 중 서로 통신할 수 있는 쌍이 있는지, 있다면 통신 비용의 최댓값은 얼마인지를 알려주는 프로그램을 작성하여라.

입력

표준 입력에서 다음과 같은 형식으로 주어진다. 모든 값은 정수이다.

$N$

$H_1$ $A_1$ $B_1$

$\vdots$

$H_N$ $A_N$ $B_N$

$Q$

$L_1$ $R_1$

$\vdots$

$L_Q$ $R_Q$

출력

표준 출력으로 $Q$개의 줄을 출력하여라. $j$번째 ($1 \le j \le Q$)줄은 $L_j, \ L_j +1, \cdots, R_j$번 안테나 중 서로 통신할 수 있는 쌍이 없으면 -1, 있다면 통신 비용의 최댓값이어야 한다.

제한

  • $2 \le N \le 200\ 000$.
  • $0 \le H_i \le 1\ 000\ 000\ 000$ ($1 \le i \le N$).
  • $1 \le A_i \le B_i \le N-1$ ($1 \le i \le N$).
  • $1 \le Q \le 200\ 000$.
  • $1 \le L_j < R_j \le N$ ($1 \le j \le Q$).

서브태스크

번호배점제한
12

N ≤ 300, Q ≤ 300.

211

N ≤ 2 000.

322

Q = 1, L1 = 1, R1 = N.

465

No additional constraints.

예제 입력 1

5
10 2 4
1 1 1
2 1 3
1 1 1
100 1 1
5
1 2
2 3
1 3
1 4
1 5

예제 출력 1

-1
1
8
8
99

1번 안테나와 2번 안테나는 서로 통신할 수 없으므로, 첫 번째 불만에 대한 답은 -1이다.

두 번째, 세 번째, 네 번째, 다섯 번째 불만에 대한 최대 통신 비용을 가진 안테나 쌍은 각각 (2, 3), (1, 3), (1, 3), (4, 5) 이다.

예제 입력 2

20
260055884 2 15
737689751 5 5
575359903 1 15
341907415 14 14
162026576 9 19
55126745 10 19
95712405 11 14
416027186 8 13
370819848 11 14
629309664 4 13
822713895 5 15
390716905 13 17
577166133 8 19
195931195 10 17
377030463 14 17
968486685 11 19
963040581 4 10
566835557 1 12
586336111 6 16
385865831 8 9
1
1 20

예제 출력 2

806460109
[{"problem_id":"17671","problem_lang":"0","title":"\ub450 \uc548\ud14c\ub098","description":"<p>1\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0\uc758 \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\ub294 $N$\uac1c\uc758 \uc548\ud14c\ub098\uac00 \uc77c\ub82c\ub85c \ub193\uc5ec \uc788\ub2e4. \uac01 \uc548\ud14c\ub098\ub294 \ub2e4\ub978 \uc5f0\uc18d\ub41c \uc548\ud14c\ub098\uc640 1km \ub5a8\uc5b4\uc838 \uc788\ub2e4. $i$\ubc88 ($1 \\le i \\le N$) \uc548\ud14c\ub098\uc758 \ub192\uc774\ub294 $H_i$\uc774\ub2e4. $i$\ubc88 \uc548\ud14c\ub098\ub294 \uc790\uc2e0\uc73c\ub85c \ubd80\ud130 $A_i$km \uc774\uc0c1 $B_i$km \uc774\ud558 \ub5a8\uc5b4\uc838 \uc788\ub294 \uc548\ud14c\ub098\uc5d0\uac8c\ub9cc \uc815\ubcf4\ub97c \ubcf4\ub0bc \uc218 \uc788\ub2e4. \ub9cc\uc57d $x$\ubc88 \uc548\ud14c\ub098\uc640 $y$\ubc88 \uc548\ud14c\ub098\uac00 ($1 \\le x &lt; y \\le N$) \uc11c\ub85c \uc815\ubcf4\ub97c \uc8fc\uace0 \ubc1b\uc744 \uc218 \uc788\ub2e4\uba74, \uc774 \ub458\uc740 \ud1b5\uc2e0\ud560 \uc218 \uc788\uace0, \ud1b5\uc2e0 \ube44\uc6a9\uc740 $|H_x - H_y|$\uc774\ub2e4.<\/p>\r\n\r\n<p>JOI \uacf5\ud654\uad6d\uc758 \uc218\uc0c1 K\uc528\ub294 \uc2dc\ubbfc\ub4e4\ub85c\ubd80\ud130 \uc5f0\uacb0\uc0c1\ud0dc\uc5d0 \uad00\ud55c \ubd88\ub9cc $Q$\uac1c\ub97c \ub4e4\uc5c8\ub2e4. \uc870\uc0ac \uacb0\uacfc $j$ \ubc88\uc9f8 ($1 \\le j \\le Q$) \ubd88\ub9cc\uc740, $L_j, \\ L_j +1, \\cdots, R_j$\ubc88 \uc548\ud14c\ub098 \uc911 \ubb34\uc5b8\uac00\uac00 \uc774\uc0c1\uc774 \uc788\ub294\uac83\uc73c\ub85c \ubc1d\ud600\uc84c\ub2e4. \ub2f9\uc2e0\uc740, \uc774 \uc548\ud14c\ub098\ub4e4\uc911 \uc11c\ub85c \ud1b5\uc2e0\ud560 \uc218 \uc788\ub294 \uc548\ud14c\ub098 \uc30d\uc774 \uc788\ub294\uc9c0, \ub9cc\uc57d \uc788\ub2e4\uba74 \uadf8 \uc911 \uac00\uc7a5 \ud1b5\uc2e0 \ube44\uc6a9\uc774 \ub192\uc740 \uc30d\uc758 \ud1b5\uc2e0 \ube44\uc6a9\uc740 \uc5bc\ub9c8\uc778\uc9c0 \uc54c\uc544\ubcf4\ub294 \uc77c\uc744 \ub9e1\uc558\ub2e4.<\/p>\r\n\r\n<p>\uc548\ud14c\ub098\uc758 \uc815\ubcf4\uc640 \ubd88\ub9cc\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, $L_j, \\ L_j +1, \\cdots, R_j$\ubc88 \uc548\ud14c\ub098 \uc911 \uc11c\ub85c \ud1b5\uc2e0\ud560 \uc218 \uc788\ub294 \uc30d\uc774 \uc788\ub294\uc9c0, \uc788\ub2e4\uba74 \ud1b5\uc2e0 \ube44\uc6a9\uc758 \ucd5c\ub313\uac12\uc740 \uc5bc\ub9c8\uc778\uc9c0\ub97c \uc54c\ub824\uc8fc\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\ud45c\uc900 \uc785\ub825\uc5d0\uc11c \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \uac12\uc740 \uc815\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>$N$<\/p>\r\n\r\n<p>$H_1$ $A_1$ $B_1$<\/p>\r\n\r\n<p>$\\vdots$<\/p>\r\n\r\n<p>$H_N$ $A_N$ $B_N$<\/p>\r\n\r\n<p>$Q$<\/p>\r\n\r\n<p>$L_1$ $R_1$<\/p>\r\n\r\n<p>$\\vdots$<\/p>\r\n\r\n<p>$L_Q$ $R_Q$<\/p>\r\n","output":"<p>\ud45c\uc900 \ucd9c\ub825\uc73c\ub85c $Q$\uac1c\uc758 \uc904\uc744 \ucd9c\ub825\ud558\uc5ec\ub77c. $j$\ubc88\uc9f8 ($1 \\le j \\le Q$)\uc904\uc740 $L_j, \\ L_j +1, \\cdots, R_j$\ubc88 \uc548\ud14c\ub098 \uc911 \uc11c\ub85c \ud1b5\uc2e0\ud560 \uc218 \uc788\ub294 \uc30d\uc774 \uc5c6\uc73c\uba74 <code>-1<\/code>, \uc788\ub2e4\uba74 \ud1b5\uc2e0 \ube44\uc6a9\uc758 \ucd5c\ub313\uac12\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2 \\le N \\le 200\\ 000$.<\/li>\r\n\t<li>$0 \\le H_i \\le 1\\ 000\\ 000\\ 000$ ($1 \\le i \\le N$).<\/li>\r\n\t<li>$1 \\le A_i \\le B_i \\le N-1$ ($1 \\le i \\le N$).<\/li>\r\n\t<li>$1 \\le Q \\le 200\\ 000$.<\/li>\r\n\t<li>$1 \\le L_j &lt; R_j \\le N$ ($1 \\le j \\le Q$).<\/li>\r\n<\/ul>\r\n","subtask1":"<p>N &le; 300, Q &le; 300.<\/p>\r\n","subtask2":"<p>N &le; 2 000.<\/p>\r\n","subtask3":"<p>Q = 1, L<sub>1<\/sub> = 1, R<sub>1<\/sub> = N.<\/p>\r\n","subtask4":"<p>No additional constraints.<\/p>\r\n","sample_explain_1":"<p>1\ubc88 \uc548\ud14c\ub098\uc640 2\ubc88 \uc548\ud14c\ub098\ub294 \uc11c\ub85c \ud1b5\uc2e0\ud560 \uc218 \uc5c6\uc73c\ubbc0\ub85c, \uccab \ubc88\uc9f8 \ubd88\ub9cc\uc5d0 \ub300\ud55c \ub2f5\uc740 -1\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8, \uc138 \ubc88\uc9f8, \ub124 \ubc88\uc9f8, \ub2e4\uc12f \ubc88\uc9f8 \ubd88\ub9cc\uc5d0 \ub300\ud55c \ucd5c\ub300 \ud1b5\uc2e0 \ube44\uc6a9\uc744 \uac00\uc9c4 \uc548\ud14c\ub098 \uc30d\uc740 \uac01\uac01 (2, 3), (1, 3), (1, 3), (4, 5) \uc774\ub2e4.<\/p>\r\n"},{"problem_id":"17671","problem_lang":"1","title":"Two Antennas","description":"<p>There are N antennas, numbered from 1 to N along a line. Each antenna is one kilometer distant from consecutive antennas. The height of the antenna i (1 &le; i &le; N) is H<sub>i<\/sub>. The antenna i can send information to the antennas located between A<sub>i<\/sub> kilometers and B<sub>i<\/sub> kilometers, inclusive, from the antenna i. If and only if the antenna x and the antenna y (1 &le; x &lt; y &le; N) can send information to each other, the pair of antennas is in communication, and the communication cost is equal to |H<sub>x<\/sub> &minus; H<sub>y<\/sub>|.<\/p>\r\n\r\n<p>Mr. K, the Prime Minister of JOI Republic, has received Q complaints about bad connection from the citizens. A study showed that, for the j-th complaint (1 &le; j &le; Q), something among the antennas L<sub>j<\/sub>, L<sub>j+1<\/sub>, . . . , R<sub>j<\/sub> has troubles. You are assigned to find whether there exists a pair of antennas in communication among the antennas L<sub>j<\/sub>, L<sub>j+1<\/sub>, . . . , R<sub>j<\/sub>, and if there does, you also have to find the maximum communication cost among such pairs.<\/p>\r\n\r\n<p>Write a program which, given the information of antennas and complaints, determines whether there exists a pair of antennas in communication among the antennas L<sub>j<\/sub>, L<sub>j+1<\/sub>, . . . , R<sub>j<\/sub> and calculates the maximum communication cost among such pairs if there exists such a pair.<\/p>\r\n","input":"<p>Read the following data from the standard input. All the values in the input are integers.<\/p>\r\n\r\n<pre>\r\nN\r\nH<sub>1<\/sub> A<sub>1<\/sub> B<sub>1<\/sub>\r\n.\r\n.\r\n.\r\nH<sub>N<\/sub> A<sub>N<\/sub> B<sub>N<\/sub>\r\nQ\r\nL<sub>1<\/sub> R<sub>1<\/sub>\r\n.\r\n.\r\n.\r\nL<sub>Q<\/sub> R<sub>Q<\/sub><\/pre>\r\n","output":"<p>Write Q lines to the standard output. The j-th line (1 &le; j &le; Q) should be &minus;1 if there is no pair of antennas in communication among the antennas L<sub>j<\/sub>, L<sub>j+1<\/sub>, . . . , R<sub>j<\/sub>, or the maximum communication cost among such pairs otherwise.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>2 &le; N &le; 200 000.<\/li>\r\n\t<li>1 &le; H<sub>i<\/sub> &le; 1 000 000 000 (1 &le; i &le; N).<\/li>\r\n\t<li>1 &le; A<sub>i<\/sub> &le; B<sub>i<\/sub> &le; N &minus; 1 (1 &le; i &le; N).<\/li>\r\n\t<li>1 &le; Q &le; 200 000.<\/li>\r\n\t<li>1 &le; L<sub>j<\/sub> &lt; R<sub>j<\/sub> &le; N (1 &le; j &le; Q).<\/li>\r\n<\/ul>\r\n","subtask1":"<p>N &le; 300, Q &le; 300.<\/p>\r\n","subtask2":"<p>N &le; 2 000.<\/p>\r\n","subtask3":"<p>Q = 1, L<sub>1<\/sub> = 1, R<sub>1<\/sub> = N.<\/p>\r\n","subtask4":"<p>No additional constraints.<\/p>\r\n","sample_explain_1":"<p>The antenna 1 and the antenna 2 are not in communication, so the answer to the 1st complaint is &minus;1.<\/p>\r\n\r\n<p>The pair of antennas in communication which has the maximum communication cost for the 2nd, 3rd, 4th and 5th complaint is (2, 3), (1, 3), (1, 3), and (4, 5), respectively.<\/p>\r\n"}]

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