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D. Developing Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPavel 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.

Examples

Input

4

2 8 9

1 4 7

3 6 8

5 8 10

Output

3

1 3 4

Input

6

3 5 16

1 6 11

4 8 12

7 9 16

2 10 14

8 13 15

Output

4

1 2 3 5

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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