A9345 | Developing Game

Pavel is going to make a game of his dream. However, he knows that he can't make it on his own so he founded a development company and hired $n$ workers of staff. Now he wants to pick $n$ workers from the staff who will be directly responsible for developing a game.

Each worker has a certain skill level $v_{i}$ . Besides, each worker doesn't want to work with the one whose skill is very different. In other words, the $i$ -th worker won't work with those whose skill is less than $l_{i}$ , and with those whose skill is more than $r_{i}$ .

Pavel understands that the game of his dream isn't too hard to develop, so the worker with any skill will be equally useful. That's why he wants to pick a team of the maximum possible size. Help him pick such team.

The first line contains a single integer $n$ ( $1<=n<=10^{5}$ ) — the number of workers Pavel hired.

Each of the following $n$ lines contains three space-separated integers $l_{i}$ , $v_{i}$ , $r_{i}$ ( $1<=l_{i}<=v_{i}<=r_{i}<=3·10^{5}$ ) — the minimum skill value of the workers that the $i$ -th worker can work with, the $i$ -th worker's skill and the maximum skill value of the workers that the $i$ -th worker can work with.

In the first line print a single integer $m$ — the number of workers Pavel must pick for developing the game.

In the next line print $m$ space-separated integers — the numbers of the workers in any order.

If there are multiple optimal solutions, print any of them.