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:
//package round222;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[][] ws = new int[n][];
		for(int i = 0;i < n;i++){
			ws[i] = na(3);
		}
		int[][] rls = new int[2*n][];
		for(int i = 0;i < n;i++){
			rls[2*i] = new int[]{ws[i][0], i, 1};
			rls[2*i+1] = new int[]{ws[i][1]+1, i, -1};
		}
		Arrays.sort(rls, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[0] != b[0])return a[0] - b[0];
				return a[2] - b[2];
			}
		});
		
		int W = 300001;
		StarrySkyTree sst = new StarrySkyTree(W);
		int bestTime = -1;
		int max = 0;
		int maxpos = -1;
		for(int i = 0;i < rls.length;i++){
			int[] rl = rls[i];
			sst.add(ws[rl[1]][1], ws[rl[1]][2]+1, -rl[2]);
			int v = -sst.st[1];
			if(v > max){
				max = v;
				maxpos = sst.pos[1];
				bestTime = i;
			}
		}
		
		out.println(max);
		int[] ok = new int[n];
		for(int i = 0;i <= bestTime;i++){
			int[] rl = rls[i];
			if(ws[rl[1]][1] <= maxpos && maxpos <= ws[rl[1]][2]){
				ok[rl[1]] += rl[2];
			}
		}
		for(int i = 0;i < n;i++){
			if(ok[i] > 0){
				out.print(i+1 + " ");
			}
		}
		out.println();
	}
	
	public static class StarrySkyTree {
		public int M, H, N;
		public int[] st;
		public int[] plus;
		public int[] pos;
		public int I = Integer.MAX_VALUE/4; // I+plus<int
		
		public StarrySkyTree(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			plus = new int[H];
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		public StarrySkyTree(int[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			Arrays.fill(st, H+N, M, I);
			plus = new int[H];
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			if(st[2*i] <= st[2*i+1]){
				st[i] = st[2*i] + plus[i];
				pos[i] = pos[2*i];
			}else{
				st[i] = st[2*i+1] + plus[i];
				pos[i] = pos[2*i+1];
			}
		}
		
		public void add(int l, int r, int v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, int v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(Math.max(l, cl) < Math.min(r, mid)){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(Math.max(l, mid) < Math.min(r, cr)){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public int min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private int min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				int ret = I;
				if(Math.max(l, cl) < Math.min(r, mid)){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(Math.max(l, mid) < Math.min(r, cr)){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public int[] toArray() { return toArray(1, 0, H, new int[H]); }
		
		private int[] toArray(int cur, int l, int r, int[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}