Ezzat and Grid

Description:

Input:

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.

Output:

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.

Sample Input:

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

Sample Output:

0

Sample Input:

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

Sample Output:

3
2 4 5

Note:

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: