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.

Input

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.

Output

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.