시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 256 MB 182 76 43 43.434%

문제

크기 n의 순열은, 1부터 n까지의 정수가 정확히 한 번 등장하는 길이 n의 수열을 뜻한다. 이 순열을 a1, a2, ..., an 으로 표기하자. 순열 a를 통해서 순열 그래프를 만들 수 있다. 순열 그래프는 1, 2, ..., n의 번호를 가진 n개의 정점으로 이루어진 무방향 그래프이다. 순열 그래프의 두 정점 쌍 i, j (1 ≤ i < j ≤ n) 는 ai > aj 일때 간선으로 연결되어 있다.

순열 그래프의 연결성을 판별하기 위해서, 당신은 순열 그래프를 다음과 같은 알고리즘으로 탐색해야 한다.

  1. 1번 정점부터 순서대로 n번 정점까지 순회한다. 현재 처리 중인 정점을 i 번 정점이라고 하자.
  2. i번 정점이 이전에 탐색되었다면, 넘어간다. 그렇지 않다면, i번 정점과 연결된 모든 정점을 탐색한 후, 탐색한 정점을 모아 집합을 하나 만든다.
  3. 최종적으로, 구한 집합의 총 개수와, 각 집합의 정보를 출력한다.

알고리즘을 읽은 동욱이는, 이 문제가 그래프의 연결 컴포넌트를 구하는 쉬운 문제임을 알게 되었다. 동욱이는 재현이에게 ”이거 깊이 우선 탐색으로 풀면 돼?” 라고 물었다. 재현이는 아무 대답도 하지 않았다. 당신은 어떻게 생각하는가?

입력

첫 번째 줄에 순열의 길이 n (1 ≤ n ≤ 1, 000, 000)이 주어진다.

두 번째 줄에 n개의 공백으로 구분된 정수가 주어진다. 순열의 원소 a1, a2, ..., an 을 뜻한다.

출력

첫 번째 줄에 구한 집합의 개수 m을 출력한다.

이후 m개의 줄에 걸쳐 각각의 집합을 출력한다. 첫 번째로 집합의 크기 si를 출력하고, 이후 그 집합에 속한 si개의 정점의 번호를 공백으로 구분하여 출력한다. 정점의 번호는 오름차순으로 출력한다.

여러 개의 집합을 출력할 때, 집합에 속한 가장 작은 번호의 정점을 기준으로 오름차순으로 출력하라.

예제 입력 1

4
2 3 1 4

예제 출력 1

2
3 1 2 3
1 4

힌트

예제의 순열 그래프를 그리면 다음과 같다.

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Let V = {1, 2, ..., n} be the set of vertices. The description of a graph is given as a permutation a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>n<\/sub> of the set V (that is, a sequence of distinct numbers from V ). The vertices ai and aj are connected by an edge if the pair (i, j) forms an inversion in the permutation, that is, i &lt; j and a<sub>i<\/sub> &gt; a<sub>j<\/sub> .<\/p>\r\n\r\n<p>For example, let n = 4 and consider the permutation 2, 3, 1, 4. From this permutation we obtain the following graph:<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/7982\/1.png\" style=\"height:45px; width:153px\" \/><\/p>\r\n\r\n<p>Byteasar would like to check if the representation that he invented is useful indeed. He has decided to write a program that finds all the connected components of the graph. Recall that two vertices u; v &isin; V belong to the same connected component if there exists a sequence of vertices starting with u and ending with v such that every two subsequent vertices in the sequence are connected by an edge. In our example we have two connected components: {1, 2, 3} and {4}.<\/p>\r\n\r\n<p>Help Byteasar!<\/p>\r\n","input":"<p>The first line of input contains one integer n (1 &le; n &le; 1 000 000), the number of vertices of the graph. The second line contains n integers a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>n<\/sub>.<\/p>\r\n","output":"<p>The first line of output should contain the number of connected components in the graph. Denote this number by m. Each of the following m lines should hold a description of one connected component. First a number k should be written: the size of the component. Then, an increasing sequence of k vertex numbers of the component should be written. The components should be listed in such order that the numbers of the first nodes of the components form an increasing sequence. In other words, if S and S&prime; are two connected components, u &isin; S, v &isin; S&prime; are their nodes with the smallest number and u &lt; v, then the component S should be listed earlier than S&prime;.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]