You are playing a board card game. In this game the player has two characteristics, x and y — the white magic skill and the black magic skill, respectively. There are n spell cards lying on the table, each of them has four characteristics, ai, bi, ci and di. In one move a player can pick one of the cards and cast the spell written on it, but only if first two of it's characteristics meet the requirement ai ≤ x and bi ≤ y, i.e. if the player has enough magic skill to cast this spell. However, after casting the spell the characteristics of a player change and become equal to x = ci and y = di.

At the beginning of the game both characteristics of a player are equal to zero. The goal of the game is to cast the n-th spell. Your task is to make it in as few moves as possible. You are allowed to use spell in any order and any number of times (for example, you may not use some spells at all).

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of cards on the table.

Each of the next n lines contains four integers ai, bi, ci, di (0 ≤ ai, bi, ci, di ≤ 109) — the characteristics of the corresponding card.

Output

In the first line print a single integer k — the minimum number of moves needed to cast the n-th spell and in the second line print k numbers — the indices of the cards in the order in which you should cast them. In case there are multiple possible solutions, print any of them.

If it is impossible to cast the n-th spell, print  - 1.

Examples

Input

4
0 0 3 4
2 2 5 3
4 1 1 7
5 3 8 8


Output

3
1 2 4


Input

2
0 0 4 6
5 1 1000000000 1000000000


Output

-1
//package round335;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.Queue;

public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[][] co = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = na(4);
		}
		int[][] sco = new int[2*n][];
		int[] iind0 = new int[n];
		int p = 0;
		for(int i = 0;i < n;i++){
			sco[p++] = new int[]{co[i][0], co[i][1], i, 0};
			sco[p++] = new int[]{co[i][2], co[i][3], i, 1};
		}
		Arrays.sort(sco, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[0] != b[0])return a[0] - b[0];
				if(a[1] != b[1])return a[1] - b[1];
				return a[3] - b[3];
			}
		});
		for(int i = 0;i < 2*n;i++){
			if(sco[i][3] == 1){
			}else{
				iind0[sco[i][2]] = i;
			}
		}
		
		int[] ys = new int[2*n];
		for(int i = 0;i < 2*n;i++){
			if(sco[i][3] == 1 && sco[i][2] < n-1){
				ys[i] = -sco[i][1];
			}else{
				ys[i] = Integer.MAX_VALUE / 2;
			}
		}
		SegmentTreeRMQ st = new SegmentTreeRMQ(ys);
		Queue<Integer> q = new ArrayDeque<Integer>();
		q.add(n-1);
		int[] dp = new int[n];
		Arrays.fill(dp, 999999);
		dp[n-1] = 0;
		int[] prev = new int[n];
		Arrays.fill(prev, -1);
		while(!q.isEmpty()){
			int cur = q.poll();
			while(true){
				int fl = st.firstle(iind0[cur], -co[cur][1]);
				if(fl == -1)break;
				assert dp[sco[fl][2]] == 999999;
				dp[sco[fl][2]] = dp[cur] + 1;
				q.add(sco[fl][2]);
				st.update(fl, Integer.MAX_VALUE / 3);
				prev[sco[fl][2]] = cur;
			}
		}
		int ret = 999999;
		int start = -1;
		for(int i = 0;i < n;i++){
			if(co[i][0] == 0 && co[i][1] == 0 && dp[i] < ret){
				ret = dp[i];
				start = i;
			}
		}
		if(start == -1){
			out.println(start);
		}else{
			out.println(ret+1);
			while(start != -1){
				out.print((start+1) + " ");
				start = prev[start];
			}
			out.println();
		}
	}
	
	public static class SegmentTreeRMQ {
		public int M, H, N;
		public int[] st;
		
		public SegmentTreeRMQ(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new int[M];
			Arrays.fill(st, 0, M, Integer.MAX_VALUE);
		}
		
		public SegmentTreeRMQ(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, Integer.MAX_VALUE);
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		public void update(int pos, int x)
		{
			st[H+pos] = x;
			for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
		}
		
		private void propagate(int i)
		{
			st[i] = Math.min(st[2*i], st[2*i+1]);
		}
		
		public int minx(int l, int r){
			if(l >= r)return 0;
			int min = Integer.MAX_VALUE;
			while(l != 0){
				int f = l&-l;
				if(l+f > r)break;
				int v = st[(H+l)/f];
				if(v < min)min = v;
				l += f;
			}
			
			while(l < r){
				int f = r&-r;
				int v = st[(H+r)/f-1];
				if(v < min)min = v;
				r -= f;
			}
			return min;
		}
		
		public int min(int l, int r){ return l >= r ? 0 : 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 = Integer.MAX_VALUE;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret;
			}
		}
		
		public int firstle(int l, int v) {
			int cur = H+l;
			while(true){
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur;
					}else{
						return cur-H;
					}
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					if((cur&1)==0)cur>>>=1;
				}
			}
		}
		
		public int lastle(int l, int v) {
			int cur = H+l;
			while(true){
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur+1;
					}else{
						return cur-H;
					}
				}else{
					if((cur&cur-1) == 0)return -1;
					cur--;
					if((cur&1)==1)cur>>>=1;
				}
			}
		}
	}

	
	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)); }
}
