No submission language available for this problem.

Description

Input

The first line contains two integers $n$ and $q$ ($1 \leq n, q \leq 10^{4}$) — the length of the array and the number of queries in the initial problem.

The following $q$ lines contain queries, one per line. The $i$-th of these lines contains three integers $l_i$, $r_i$ and $x_i$ ($1 \leq l_i \leq r_i \leq n$, $1 \leq x_i \leq n$), denoting a query of adding $x_i$ to the segment from $l_i$-th to $r_i$-th elements of the array, inclusive.

Output

In the first line print the only integer $k$, denoting the number of integers from $1$ to $n$, inclusive, that can be equal to the maximum in the array after applying some subset (possibly empty) of the given operations.

In the next line print these $k$ integers from $1$ to $n$ — the possible values of the maximum. Print these integers in increasing order.

Samples

4 3
1 3 1
2 4 2
3 4 4

4
1 2 3 4 

7 2
1 5 1
3 7 2

3
1 2 3 

10 3
1 1 2
1 1 3
1 1 6

6
2 3 5 6 8 9 

Note

Consider the first example. If you consider the subset only of the first query, the maximum is equal to $1$. If you take only the second query, the maximum equals to $2$. If you take the first two queries, the maximum becomes $3$. If you take only the fourth query, the maximum becomes $4$. If you take the fourth query and something more, the maximum becomes greater that $n$, so you shouldn't print it.

In the second example you can take the first query to obtain $1$. You can take only the second query to obtain $2$. You can take all queries to obtain $3$.

In the third example you can obtain the following maximums:

• You can achieve the maximim of $2$ by using queries: $(1)$.
• You can achieve the maximim of $3$ by using queries: $(2)$.
• You can achieve the maximim of $5$ by using queries: $(1, 2)$.
• You can achieve the maximim of $6$ by using queries: $(3)$.
• You can achieve the maximim of $8$ by using queries: $(1, 3)$.
• You can achieve the maximim of $9$ by using queries: $(2, 3)$.