K. Knights
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

We all know that the Middle Ages were a time of lords, vassals, and of course, knights. In this task, you need to solve a very important question: which of the $$$N$$$ courtiers should become knights, the defenders of the kingdom.

For convenience, let's assign numbers to the courtiers from $$$1$$$ to $$$N$$$. Each courtier, except for the king, is subordinate to exactly one courtier. The king is assigned the number one and does not obey anyone. For each courtier, the subordinate courtiers (vassals) are known, as well as two numbers $$$L$$$ and $$$R$$$. These numbers imply that the retinue of this courtier must contain at least $$$L$$$ and at most $$$R$$$ knights. The retinue of a courtier includes all knights who are directly or indirectly subordinate to him, and of course, he himself if he is a knight.

More formally, a knight $$$Y$$$ is subordinate to a courtier $$$X$$$ if there exists a sequence $$$a_1, a_2, \ldots, a_j$$$ such that $$$a_1$$$ is subordinate to $$$X$$$, $$$a_2$$$ is subordinate to $$$a_1$$$, and so on, with $$$Y$$$ being subordinate to $$$a_j$$$. It is guaranteed that it is possible to select knights in such a way that the specified condition is satisfied.

Input

The first line of the input contains the number $$$N$$$ ($$$1 \leq N \leq 2 \cdot 10^5$$$) — the number of courtiers.

Each of the following $$$N$$$ lines describes the $$$i$$$-th courtier: $$$L_i$$$, $$$R_i$$$ (the minimum and maximum size of the retinue), $$$K_i$$$ ($$$0 \leq K_i \leq 2 \cdot 10^5, 0 \leq L \leq R \leq 10^9$$$). After that, there are $$$K_i$$$ numbers — the list of vassals of the $$$i$$$-th courtier (vassals can be numbered from $$$2$$$ to $$$N$$$, different from $$$i$$$, and each number appears exactly once in the input file). It is guaranteed that an answer exists and each courtier is directly or indirectly subordinate to the king, who has the number $$$1$$$.

Output

Print in the first line the number $$$M$$$ ($$$0 \leq M \leq N$$$) — the number of knights. In the next line, print $$$M$$$ distinct numbers ($$$1 \leq M_i \leq N$$$) — the numbers of the courtiers who should become knights. If there are multiple answers, you may print any.

Examples
Input
1
1 1 0
Output
1
1
Input
5
2 2 2 2 3
0 2 2 4 5
0 0 0
1 1 0
0 1 0
Output
2
4 5
Input
4
4 4 1 2
0 3 1 3
0 2 1 4
0 1 0
Output
4
1 2 3 4
Note

In the first test, the king is forced to become a knight.

In the second test, courtiers $$$2$$$ and $$$4$$$ can become knights. Then the king and courtier $$$2$$$ will have $$$2$$$ knights in their retinue. Courtiers $$$3$$$ and $$$5$$$ will have no knights at all. Courtier $$$4$$$ will have exactly 1 knight — himself.

In the third test, the king requires $$$4$$$ knights, and thus all courtiers will have to become knights and join his retinue.