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문제

두 명이 같이 하는 인터넷 슈팅 게임이 있다. 이 게임은 폐허가 된 도시에서 빌딩들을 부수는 게임이다. 게임에서 바닥인 수평선 위에 $N$개의 빌딩이 왼쪽에서 오른쪽으로 서 있다. 빌딩은 왼쪽에서 오른쪽으로 순서대로 1부터 $N$의 정수로 나타낸다. 각 빌딩의 바닥으로부터의 높이는 수열 $A_i$ $(1 \le i \le N)$로 나타내고, $1$부터 $N$까지의 서로 다른 정수로 주어진다. 

두 명의 플레이어는 모든 빌딩보다 왼쪽의 같은 위치에 있다. 시간 $i$($\ge 1$)에 두 명의 플레이어는 동시에 각 한발씩 총을 발사하고, 총알은 발사한 위치에서 수평으로 오른쪽으로 날아간다. 두 총알의 속도는 동일하다. 플레이어는 총알의 발사 높이를 바닥으로부터의 거리 $H$로 결정한다. $H$는 $1$이상 $N+1$이하의 정수이다. 두 플레이어는 동일한 발사 높이를 선택할 수 있다. 

플레이어의 총알 발사 높이가 $H$인 경우, $A_i \ge H$를 만족하는 파괴되지 않은 가장 왼쪽의 빌딩이 이 총알로 파괴된다. 이 조건을 만족하는 빌딩이 없다면, 아무 일도 일어나지 않는다. 만약 두 플레이어가 발사한 총알에 대해 이 조건을 만족하는 빌딩이 동일하다면, (두 총알의 속도는 동일하기 때문에) 이 하나의 빌딩만 파괴된다. 특별히, 두 플레이어의 발사 높이가 같다면, 항상 하나의 빌딩만 파괴된다. 예를 들어, $A_1 = 2, A_2 = 1$이고, 처음에 두 플레이어가 모두 $H = 1$을 발사 높이로 결정하였다면, 이 두 총알로 빌딩 $1$만 파괴된다. 

문제는 $N$개 빌딩들의 높이가 입력으로 주어질 때, 모든 빌딩을 파괴할 수 있는 최소 시간과 각 시간에 두 플레이어의 총알 발사 높이를 찾는 것이다.  

입력

첫째 줄에 정수 $N$이 주어진다.

다음 줄에는 $N$개의 공백으로 구분된 정수 $A_1, A_2, \ldots, A_N$이 주어진다.

출력

첫째 줄에 두 플레이어가 모든 빌딩을 파괴하기 위한 최소 시간 $T$를 출력한다.

다음 $T$개의 줄에는 공백으로 구분된 두 정수를 한 줄에 하나씩 출력한다. 두 정수는 각각 첫 번째와 두 번째 플레이어의 총알 발사 높이를 나타낸다. 두 정수는 1보다 크거나 같고, $N+1$보다 작거나 같아야 하며, 두 정수가 서로 같아도 된다.

제한

  • $1 \le N \le 100\,000$
  • $1 \le A_i \le N$ $(1 \le i \le N)$
  • $A_i$ $(1 \le i \le N)$는 모두 서로 다르다.

서브태스크

번호배점제한
117

$1 \le i < j < k \le N$이고 $A_i < A_j < A_k$를 만족하는 $(i, j, k)$가 존재하지 않는다.

212

$1 \le i < j < k \le N$이고 $A_i > A_j > A_k$를 만족하는 $(i, j, k)$가 존재하지 않는다.

39

$N \le 4$

412

$N \le 16$

531

$N \le 500$

629

$N \le 7\,500$

740

추가적인 제약 조건이 없다.

예제 입력 1

4
1 2 4 3

예제 출력 1

2
1 4
2 3

예제 입력 2

8
4 3 8 2 1 7 6 5

예제 출력 2

4
4 8
3 7
2 6
1 5

예제 입력 3

8
5 6 7 1 2 8 3 4

예제 출력 3

4
5 6
7 8
1 2
3 4
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\uba85\uc758 \ud50c\ub808\uc774\uc5b4\ub294 \ubaa8\ub4e0 \ube4c\ub529\ubcf4\ub2e4 \uc67c\ucabd\uc758 \uac19\uc740 \uc704\uce58\uc5d0 \uc788\ub2e4. \uc2dc\uac04 $i$($\\ge 1$)\uc5d0 \ub450 \uba85\uc758 \ud50c\ub808\uc774\uc5b4\ub294 \ub3d9\uc2dc\uc5d0 \uac01 \ud55c\ubc1c\uc529 \ucd1d\uc744 \ubc1c\uc0ac\ud558\uace0, \ucd1d\uc54c\uc740 \ubc1c\uc0ac\ud55c \uc704\uce58\uc5d0\uc11c \uc218\ud3c9\uc73c\ub85c \uc624\ub978\ucabd\uc73c\ub85c \ub0a0\uc544\uac04\ub2e4. \ub450 \ucd1d\uc54c\uc758 \uc18d\ub3c4\ub294 \ub3d9\uc77c\ud558\ub2e4. \ud50c\ub808\uc774\uc5b4\ub294 \ucd1d\uc54c\uc758 \ubc1c\uc0ac \ub192\uc774\ub97c \ubc14\ub2e5\uc73c\ub85c\ubd80\ud130\uc758 \uac70\ub9ac $H$\ub85c \uacb0\uc815\ud55c\ub2e4. $H$\ub294 $1$\uc774\uc0c1 $N+1$\uc774\ud558\uc758 \uc815\uc218\uc774\ub2e4. \ub450 \ud50c\ub808\uc774\uc5b4\ub294 \ub3d9\uc77c\ud55c \ubc1c\uc0ac \ub192\uc774\ub97c \uc120\ud0dd\ud560 \uc218 \uc788\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud50c\ub808\uc774\uc5b4\uc758 \ucd1d\uc54c \ubc1c\uc0ac \ub192\uc774\uac00 $H$\uc778 \uacbd\uc6b0, $A_i \\ge H$\ub97c \ub9cc\uc871\ud558\ub294 \ud30c\uad34\ub418\uc9c0 \uc54a\uc740 \uac00\uc7a5 \uc67c\ucabd\uc758 \ube4c\ub529\uc774 \uc774 \ucd1d\uc54c\ub85c \ud30c\uad34\ub41c\ub2e4. \uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ube4c\ub529\uc774 \uc5c6\ub2e4\uba74, \uc544\ubb34 \uc77c\ub3c4 \uc77c\uc5b4\ub098\uc9c0 \uc54a\ub294\ub2e4. \ub9cc\uc57d \ub450 \ud50c\ub808\uc774\uc5b4\uac00 \ubc1c\uc0ac\ud55c \ucd1d\uc54c\uc5d0 \ub300\ud574 \uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ube4c\ub529\uc774 \ub3d9\uc77c\ud558\ub2e4\uba74, (\ub450 \ucd1d\uc54c\uc758 \uc18d\ub3c4\ub294 \ub3d9\uc77c\ud558\uae30 \ub54c\ubb38\uc5d0) \uc774 \ud558\ub098\uc758 \ube4c\ub529\ub9cc \ud30c\uad34\ub41c\ub2e4. \ud2b9\ubcc4\ud788, \ub450 \ud50c\ub808\uc774\uc5b4\uc758 \ubc1c\uc0ac \ub192\uc774\uac00 \uac19\ub2e4\uba74, \ud56d\uc0c1 \ud558\ub098\uc758 \ube4c\ub529\ub9cc \ud30c\uad34\ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, $A_1 = 2, A_2 = 1$\uc774\uace0, \ucc98\uc74c\uc5d0 \ub450 \ud50c\ub808\uc774\uc5b4\uac00 \ubaa8\ub450 $H = 1$\uc744 \ubc1c\uc0ac \ub192\uc774\ub85c \uacb0\uc815\ud558\uc600\ub2e4\uba74, \uc774 \ub450 \ucd1d\uc54c\ub85c \ube4c\ub529 $1$\ub9cc \ud30c\uad34\ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ubb38\uc81c\ub294 $N$\uac1c \ube4c\ub529\ub4e4\uc758 \ub192\uc774\uac00 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c8 \ub54c, \ubaa8\ub4e0 \ube4c\ub529\uc744 \ud30c\uad34\ud560 \uc218 \uc788\ub294 \ucd5c\uc18c \uc2dc\uac04\uacfc \uac01 \uc2dc\uac04\uc5d0 \ub450 \ud50c\ub808\uc774\uc5b4\uc758 \ucd1d\uc54c \ubc1c\uc0ac \ub192\uc774\ub97c \ucc3e\ub294 \uac83\uc774\ub2e4. &nbsp;<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 $N$\uac1c\uc758 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc815\uc218&nbsp;$A_1, A_2, \\ldots, A_N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \ud50c\ub808\uc774\uc5b4\uac00 \ubaa8\ub4e0 \ube4c\ub529\uc744 \ud30c\uad34\ud558\uae30 \uc704\ud55c \ucd5c\uc18c \uc2dc\uac04 $T$\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $T$\uac1c\uc758 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \ub450 \uc815\uc218\ub97c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4. \ub450 \uc815\uc218\ub294 \uac01\uac01 \uccab \ubc88\uc9f8\uc640 \ub450 \ubc88\uc9f8 \ud50c\ub808\uc774\uc5b4\uc758 \ucd1d\uc54c \ubc1c\uc0ac \ub192\uc774\ub97c \ub098\ud0c0\ub0b8\ub2e4. \ub450 \uc815\uc218\ub294 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, $N+1$\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc544\uc57c \ud558\uba70, \ub450 \uc815\uc218\uac00 \uc11c\ub85c \uac19\uc544\ub3c4 \ub41c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\le N \\le 100\\,000$<\/li>\r\n\t<li>$1 \\le A_i \\le N$ $(1 \\le i \\le N)$<\/li>\r\n\t<li>$A_i$ $(1 \\le i \\le N)$\ub294 \ubaa8\ub450 \uc11c\ub85c \ub2e4\ub974\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$1 \\le i &lt; j &lt; k \\le N$\uc774\uace0 $A_i &lt; A_j &lt; A_k$\ub97c \ub9cc\uc871\ud558\ub294 $(i, j, k)$\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","subtask2":"<p>$1 \\le i &lt; j &lt; k \\le N$\uc774\uace0 $A_i &gt; A_j &gt; A_k$\ub97c \ub9cc\uc871\ud558\ub294 $(i, j, k)$\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","subtask3":"<p>$N \\le 4$<\/p>\r\n","subtask4":"<p>$N \\le 16$<\/p>\r\n","subtask5":"<p>$N \\le 500$<\/p>\r\n","subtask6":"<p>$N \\le 7\\,500$<\/p>\r\n","subtask7":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"22030","problem_lang":"1","title":"Two Bullets","description":"<p>There is a two-person video game about destroying buildings in a ruined city. In the game, there are $N$ buildings over a flat ground. Buildings are indexed from $1$ to $N$ in left to right order. The height of building $i$ is $A_i$ $(1 \\le i \\le N)$, which is a positive integer in range $1$ to $N$. No two buildings have the same height.&nbsp;<\/p>\r\n\r\n<p>Initially, both players are to the left of all buildings. At time $i$($\\ge 1$), both players fire one shot each at the same time, and the bullets fly horizontally to the right from where they were fired. Both bullets have the same speed. The player selects the bullet&#39;s firing height as the distance $H$ from the floor. $H$ is an integer in range $1$ to $N + 1$. Both players can choose the same height.<\/p>\r\n\r\n<p>If the player&#39;s bullet firing height is $H$, the leftmost un-destroyed building that satisfies $A_i \\ge H$ will be destroyed by this bullet. If no building satisfies this condition, nothing happens. If the building that satisfies this condition for the bullets fired by both players is the same, only this one building is destroyed (since both bullets have the same velocity). In particular, if both players have the same launch height, only one building can be destroyed. For example, if $A_1 = 2, A_2 = 1$, and both players initially set $H = 1$ as the firing height, building 1 will be destroyed, but building 2 will stay in place.<\/p>\r\n\r\n<p>Given the heights of $N$ buildings, find the minimum time to destroy all the buildings, and provide any sequence of firing heights which achieves this.<\/p>\r\n","input":"<p>The first line contains a single integer $N$. ($1 \\le N \\le 100\\,000$)<\/p>\r\n\r\n<p>The next line contains $N$ space-separated integer $A_1, A_2, \\ldots, A_N$. ($1 \\le A_i \\le N$). All $A_i$&#39;s are distinct.<\/p>\r\n","output":"<p>In the first line, print a single integer $T$ denoting the minimum time.<\/p>\r\n\r\n<p>In next $T$ lines, print two space-separated integers denoting the firing heights of both players. Both integers should be at least 1, and at most $N+1$. Both integers can be equal.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","subtask1":"<p>There exists no tuple $(i, j, k)$ such that $1 \\le i &lt; j &lt; k \\le N$ and $A_i &lt; A_j &lt; A_k$ holds.<\/p>\r\n","subtask2":"<p>There exists no tuple $(i, j, k)$ such that $1 \\le i &lt; j &lt; k \\le N$ and $A_i &gt; A_j &gt; A_k$ holds.<\/p>\r\n","subtask3":"<p>$N \\le 4$<\/p>\r\n","subtask4":"<p>$N \\le 16$<\/p>\r\n","subtask5":"<p>$N \\le 500$<\/p>\r\n","subtask6":"<p>$N \\le 7\\,500$<\/p>\r\n","subtask7":"<p>No additional limits.<\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.
  • 이 문제의 채점 우선 순위는 2이다.