# Ezzat and Grid

## 题意翻译

* 有一个 $n$ 行 $10^9$ 列的表格。 * dead_X 会执行 $m$ 次操作，每次操作会将第 $i$ 行的第 $[l,r]$ 格涂黑。 * dead_X 想知道，至少删掉几行后，对于每相邻的两行，都存在**至少一列**，使得这两行的这一列都涂黑了。 * $n,m\leq3\times 10^5$，一个格子可能被涂黑多次。

## 题目描述

Moamen was drawing a grid of $n$ rows and $10^9$ columns containing only digits $0$ and $1$ . Ezzat noticed what Moamen was drawing and became interested in the minimum number of rows one needs to remove to make the grid beautiful. A grid is beautiful if and only if for every two consecutive rows there is at least one column containing $1$ in these two rows. Ezzat will give you the number of rows $n$ , and $m$ segments of the grid that contain digits $1$ . Every segment is represented with three integers $i$ , $l$ , and $r$ , where $i$ represents the row number, and $l$ and $r$ represent the first and the last column of the segment in that row. For example, if $n = 3$ , $m = 6$ , and the segments are $(1,1,1)$ , $(1,7,8)$ , $(2,7,7)$ , $(2,15,15)$ , $(3,1,1)$ , $(3,15,15)$ , then the grid is: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1557D/9e4ccafba8e9c07a0c3a14a574b9d7c53033cfd0.png)Your task is to tell Ezzat the minimum number of rows that should be removed to make the grid beautiful.

## 输入输出格式

### 输入格式

The first line contains two integers $n$ and $m$ ( $1 \le n, m \le 3\cdot10^5$ ). Each of the next $m$ lines contains three integers $i$ , $l$ , and $r$ ( $1 \le i \le n$ , $1 \le l \le r \le 10^9$ ). Each of these $m$ lines means that row number $i$ contains digits $1$ in columns from $l$ to $r$ , inclusive. Note that the segments may overlap.

### 输出格式

In the first line, print a single integer $k$ — the minimum number of rows that should be removed. In the second line print $k$ distinct integers $r_1, r_2, \ldots, r_k$ , representing the rows that should be removed ( $1 \le r_i \le n$ ), in any order. If there are multiple answers, print any.

## 输入输出样例

### 输入样例 #1

3 6
1 1 1
1 7 8
2 7 7
2 15 15
3 1 1
3 15 15

### 输出样例 #1

0

### 输入样例 #2

5 4
1 2 3
2 4 6
3 3 5
5 1 1

### 输出样例 #2

3
2 4 5

## 说明

In the first test case, the grid is the one explained in the problem statement. The grid has the following properties: 1. The $1$ -st row and the $2$ -nd row have a common $1$ in the column $7$ . 2. The $2$ -nd row and the $3$ -rd row have a common $1$ in the column $15$ . As a result, this grid is beautiful and we do not need to remove any row.In the second test case, the given grid is as follows: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1557D/8652918b2f57efcbbbd2515fe51b146893b7cc96.png)