Problem: 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 vi. 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 li, and with those whose skill is more than ri.

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 ≤ 105) — the number of workers Pavel hired.

Each of the following n lines contains three space-separated integers li, vi, ri (1 ≤ li ≤ vi ≤ ri ≤ 3·105) — 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

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class D {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	static final int M = 300000;

	static class Node {
		int l, r;
		Node left, right;
		int max, maxPos;
		int add;

		public Node(int l, int r) {
			this.l = l;
			this.r = r;
			max = 0;
			maxPos = l;
			if (r - l > 1) {
				int mid = (l + r) >> 1;
				left = new Node(l, mid);
				right = new Node(mid, r);
			}
		}

		int getMax() {
			return max + add;
		}

		void add(int ql, int qr, int delta) {
			if (ql >= r || l >= qr) {
				return;
			}
			if (ql <= l && r <= qr) {
				add += delta;
				return;
			}
			left.add(ql, qr, delta);
			right.add(ql, qr, delta);
			if (left.getMax() >= right.getMax()) {
				max = left.getMax();
				maxPos = left.maxPos;
			} else {
				max = right.getMax();
				maxPos = right.maxPos;
			}
		}
	}

	static class Worker {
		int l, self, r, ind;

		public Worker(int l, int self, int r) {
			this.l = l;
			this.self = self;
			this.r = r;
		}
	}

	static class Event implements Comparable<Event> {
		boolean add;
		int pos;
		Worker w;

		public Event(boolean add, int pos, Worker w) {
			this.add = add;
			this.pos = pos;
			this.w = w;
		}

		@Override
		public int compareTo(Event o) {
			if (pos != o.pos)
				return Integer.compare(pos, o.pos);
			if (add != o.add)
				return add ? -1 : 1;
			return 0;
		}
	}

	void solve() throws IOException {
		int n = nextInt();
		Worker[] a = new Worker[n];
		Event[] ev = new Event[2 * n];
		Node root = new Node(0, M);
		for (int i = 0; i < n; i++) {
			a[i] = new Worker(nextInt() - 1, nextInt() - 1, nextInt() - 1);

			ev[2 * i] = new Event(true, a[i].l, a[i]);
			ev[2 * i + 1] = new Event(false, a[i].self, a[i]);
		}

		Arrays.sort(ev);

		int ans = 0;
		int ansPosL = -1;
		int ansPosR = -1;

		for (int i = 0; i < 2 * n; i++) {
			Event e = ev[i];
			root.add(e.w.self, e.w.r + 1, e.add ? 1 : -1);
			if (e.add) {
				if (root.max > ans) {
					ans = root.max;
					ansPosL = e.pos;
					ansPosR = root.maxPos;
				}
			}
		}

		out.println(ans);
		for (int i = 0; i < n; i++) {
			if (a[i].l <= ansPosL && a[i].self >= ansPosL
					&& a[i].self <= ansPosR && a[i].r >= ansPosR) {
				out.print(i + 1 + " ");
			}
		}
		out.println();
	}

	D() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new D();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}