시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 35 4 4 12.903%

문제

N개의 우주선이 레이스를 하고 있다. i번째 우주선은 순식간에(0초에) 최대 속도인 V[i]에 도달할 수 있고, 이 속도를 레이스가 끝날 때까지 유지할 수 있다. 또한 각 우주선은 지난 대회의 결과에 따라서 X[i]라는 출발점에서 출발하게 된다. 레이스 장은 무한히 길고 X축에 평행하다. 각각의 우주선은 X축에만 평행하게 움직인다.

이렇게 레이스를 하다 보면 우주선이 다른 우주선을 추월하는 경우도 발생하게 된다. 각각의 우주선은 X[i]좌표와는 별도로 Y, Z 좌표도 가지고 있기 때문에 충돌에 대해서는 생각할 필요가 없다.

경기가 끝날 때까지 발생하는 추월들을 알아내는 프로그램을 작성하시오. 경기는 더 이상 추월이 발생하지 않을 때까지 반복된다. 우선 추월의 회수를 알아내야 하고, 연대순으로 처음 10,000개의 추월이 구체적으로 어떤 추월인지(몇 번이 몇 번을 추월하는지)를 알아내야 한다. 편의상 모든 X[i]가 다르다고 가정하자. 또한, 매 순간에 한 x좌표에는 최대 두 개의 우주선만 있을 수 있다.

입력

첫째 줄에 우주선의 개수 N(1 ≤ N ≤ 250,000)이 주어진다. 다음 N개의 줄에는 차례로 X[1] V[1], X[2] V[2], …, X[N] V[N]이 주어진다. 이때 1 ≤ X[i] ≤ 1,000,000과 1 ≤ V[i] ≤ 99가 만족된다. 편의상 X[1] < X[2] < … < X[N]이 만족된다고 가정하자.

출력

첫째 줄에 추월의 회수를 1,000,000으로 나눈 나머지를 출력한다. 다음 줄들에는 각 추월에 대한 정보를 연대순으로(시간 순으로) 출력한다. 만약 추월 회수가 10,000을 넘어가면 처음의 10,000개만 출력하도록 한다. 각 줄은 두 개의 정수 i, j로 출력하는데, i번 우주선이 j번 우주선을 추월한다는 의미이다. 여러 추월이 동시에 일어나면 추월이 일어나는 위치가 출발점에 가까운(x좌표가 작은) 것을 먼저 출력한다.

예제 입력 1

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예제 출력 1

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Each spaceship i is tuned in such a way that it can accelerate in zero time to its maximum speed V<sub>i<\/sub> and remain cruising at that speed. Due to past achievements, each spaceship starts at a starting position X<sub>i<\/sub>, specifying how many kilometers the spaceship is away from the starting line.<\/p>\r\n\r\n<p>The race course is in\ufb01nitely long. Because of the high speeds of the spaceships, the race course goes straight all the time. On that straight course, spaceships can pass one another very easily, without interfering with each other.<\/p>\r\n\r\n<p>Many people in the audience have not realized yet that the outcome of the race can be determined in advance. It is your task to show this to them, by telling them how many times spaceships will pass one another, and by predicting the \ufb01rst 10 000 times that spaceships pass in chronological order.<\/p>\r\n\r\n<p>You may assume that each spaceship starts at a different position. Furthermore, there will never be more than two spaceships at the same position of the course at any time.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e164b7d2-dbbf-48ba-b2c2-03f80373f714\/-\/preview\/\" style=\"width: 352px; height: 179px;\" \/><\/p>\r\n","input":"<p>The \ufb01rst line of the input speci\ufb01es the number of spaceships N (0 &lt; N &le; 250 000) that are competing. Each of the next N lines describe the properties of one spaceship. The i+1th line describes the ith ship with two integers X<sub>i<\/sub> and V<sub>i<\/sub>, representing the starting position and the velocity of the ith spaceship (0 &le; X<sub>i<\/sub> &le; 1 000 000, 0 &lt; V<sub>i<\/sub> &lt; 100). The spaceships are ordered according to the starting position, i.e. X<sub>1<\/sub> &lt; X<sub>2<\/sub> &lt; . . . &lt; X<sub>N<\/sub>. The starting position is the number of kilometers past the starting line where the spaceship starts, and the velocity is given in kilometers per second.<\/p>\r\n","output":"<p>The \ufb01rst line of the output should contain the number of times that spaceships pass one another during the race modulo 1 000 000. By publishing the number of passes only modulo 1 000 000, you can at the same time prove your knowledge of it and don&rsquo;t spoil the party for the less intelligent people in the audience.<\/p>\r\n\r\n<p>Each of the subsequent lines should represent one passing, in chronological order. If there would be more than 10 000 passings, only output the \ufb01rst 10 000 passings. If there are less than 10 000 passings, output all passings. Each line should consist of two integers i and j, specifying that spaceship i passes spaceship j. If multiple passings occur at the same time, they have to be sorted by their position on the course. This means that passings taking place closer to the starting line must be listed \ufb01rst. The time of a passing is the time when the two spaceships are at the same position.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]