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
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskD {
		int[] last;
		int[] a;
		int[] b;
		int[] c;
		int[] d;
		IntQueue queue = new IntArrayQueue();
		IntList[] lists;
		int[] shift;

		public void solve(int testNumber, InputReader in, OutputWriter out) {
			int n = in.readInt();
			a = new int[n];
			b = new int[n];
			c = new int[n];
			d = new int[n];
			IOUtils.readIntArrays(in, a, b, c, d);
			a = Arrays.copyOf(a, n + 1);
			b = Arrays.copyOf(b, n + 1);
			c = Arrays.copyOf(c, n + 1);
			d = Arrays.copyOf(d, n + 1);
			ArrayUtils.compress(a, c);
			ArrayUtils.compress(b, d);
			last = new int[n + 1];
			Arrays.fill(last, -1);
			last[n] = n;
			lists = new IntList[8 * n + 4];
			shift = new int[8 * n + 4];
			init(0, 0, 2 * n);
			for (int i = 0; i < n; i++) {
				add(0, 0, 2 * n, i);
			}
			IntComparator comparator = (x, y) -> b[x] - b[y];
			for (int i = 0; i < 8 * n + 4; i++) {
				if (lists[i] != null) {
					lists[i].sort(comparator);
				}
			}
			queue.add(n);
			while (!queue.isEmpty()) {
				int current = queue.poll();
				check(0, 0, 2 * n, current);
			}
			if (last[n - 1] == -1) {
				out.printLine(-1);
				return;
			}
			IntList answer = new IntArrayList();
			int current = n - 1;
			while (current != n) {
				answer.add(current + 1);
				current = last[current];
			}
			answer.inPlaceReverse();
			out.printLine(answer.size());
			out.printLine(answer);
		}

		private void check(int root, int left, int right, int id) {
			if (left > c[id]) {
				return;
			}
			if (right <= c[id]) {
				while (shift[root] < lists[root].size()) {
					int current = lists[root].get(shift[root]);
					if (b[current] <= d[id]) {
						if (last[current] == -1) {
							last[current] = id;
							queue.add(current);
						}
						shift[root]++;
					} else {
						break;
					}
				}
				return;
			}
			int middle = (left + right) >> 1;
			check(2 * root + 1, left, middle, id);
			check(2 * root + 2, middle + 1, right, id);
		}

		private void add(int root, int left, int right, int id) {
			if (a[id] < left || a[id] > right) {
				return;
			}
			lists[root].add(id);
			if (left != right) {
				int middle = (left + right) >> 1;
				add(2 * root + 1, left, middle, id);
				add(2 * root + 2, middle + 1, right, id);
			}
		}

		private void init(int root, int left, int right) {
			lists[root] = new IntArrayList();
			if (left != right) {
				int middle = (left + right) >> 1;
				init(2 * root + 1, left, middle);
				init(2 * root + 2, middle + 1, right);
			}
		}

	}

	static interface IntIterator {
		public int value();

		public boolean advance();

		public boolean isValid();

	}

	static class IntArrayQueue implements IntQueue {
		private int[] data;
		private int from;
		private int to;

		public IntArrayQueue(int capacity) {
			data = new int[Integer.highestOneBit(capacity) << 1];
		}

		public IntArrayQueue() {
			this(3);
		}

		public IntArrayQueue(int[] array) {
			this(array.length);
			to = array.length;
			System.arraycopy(array, 0, data, 0, to);
		}

		public IntArrayQueue(IntStream s) {
			addAll(s);
		}

		public IntArrayQueue(IntCollection c) {
			this(c.size());
			addAll(c);
		}

		public int size() {
			return (to - from) & (data.length - 1);
		}

		public void add(int v) {
			ensureCapacity(size() + 1);
			data[to++] = v;
			to &= data.length - 1;
		}

		public int poll() {
			if (from == to) {
				throw new NoSuchElementException();
			}
			int result = data[from++];
			from &= data.length - 1;
			return result;
		}

		public IntIterator intIterator() {
			return new IntIterator() {
				private int at = from;

				public int value() {
					if (at == to) {
						throw new NoSuchElementException();
					}
					return data[at];
				}

				public boolean advance() {
					if (!isValid()) {
						throw new NoSuchElementException();
					}
					at++;
					at &= data.length - 1;
					return isValid();
				}

				public boolean isValid() {
					return at != to;
				}

				public void remove() {
					throw new UnsupportedOperationException();
				}
			};
		}

		private void ensureCapacity(int capacity) {
			if (data.length <= capacity) {
				int[] newData = new int[Integer.highestOneBit(capacity) << 1];
				if (from <= to) {
					System.arraycopy(data, from, newData, 0, size());
				} else {
					System.arraycopy(data, from, newData, 0, data.length - from);
					System.arraycopy(data, 0, newData, data.length - from, to);
				}
				to = size();
				from = 0;
				data = newData;
			}
		}

	}

	static interface IntQueue extends IntCollection {
		public int poll();

	}

	static class ArrayUtils {
		public static int[] sort(int[] array, IntComparator comparator) {
			return sort(array, 0, array.length, comparator);
		}

		public static int[] sort(int[] array, int from, int to, IntComparator comparator) {
			if (from == 0 && to == array.length)
				new IntArray(array).sort(comparator);
			else
				new IntArray(array).subList(from, to).sort(comparator);
			return array;
		}

		public static int[] unique(int[] array) {
			return new IntArray(array).unique().toArray();
		}

		public static int[] compress(int[]... arrays) {
			int totalLength = 0;
			for (int[] array : arrays)
				totalLength += array.length;
			int[] all = new int[totalLength];
			int delta = 0;
			for (int[] array : arrays) {
				System.arraycopy(array, 0, all, delta, array.length);
				delta += array.length;
			}
			sort(all, IntComparator.DEFAULT);
			all = unique(all);
			for (int[] array : arrays) {
				for (int i = 0; i < array.length; i++)
					array[i] = Arrays.binarySearch(all, array[i]);
			}
			return all;
		}

	}

	static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
		public IntIterator intIterator();

		default public Iterator<Integer> iterator() {
			return new Iterator<Integer>() {
				private IntIterator it = intIterator();

				public boolean hasNext() {
					return it.isValid();
				}

				public Integer next() {
					int result = it.value();
					it.advance();
					return result;
				}
			};
		}

		default public int compareTo(IntStream c) {
			IntIterator it = intIterator();
			IntIterator jt = c.intIterator();
			while (it.isValid() && jt.isValid()) {
				int i = it.value();
				int j = jt.value();
				if (i < j) {
					return -1;
				} else if (i > j) {
					return 1;
				}
				it.advance();
				jt.advance();
			}
			if (it.isValid()) {
				return 1;
			}
			if (jt.isValid()) {
				return -1;
			}
			return 0;
		}

	}

	static class Sorter {
		private static final int INSERTION_THRESHOLD = 16;

		private Sorter() {
		}

		public static void sort(IntList list, IntComparator comparator) {
			quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1, comparator);
		}

		private static void quickSort(IntList list, int from, int to, int remaining, IntComparator comparator) {
			if (to - from < INSERTION_THRESHOLD) {
				insertionSort(list, from, to, comparator);
				return;
			}
			if (remaining == 0) {
				heapSort(list, from, to, comparator);
				return;
			}
			remaining--;
			int pivotIndex = (from + to) >> 1;
			int pivot = list.get(pivotIndex);
			list.swap(pivotIndex, to);
			int storeIndex = from;
			int equalIndex = to;
			for (int i = from; i < equalIndex; i++) {
				int value = comparator.compare(list.get(i), pivot);
				if (value < 0) {
					list.swap(storeIndex++, i);
				} else if (value == 0) {
					list.swap(--equalIndex, i--);
				}
			}
			quickSort(list, from, storeIndex - 1, remaining, comparator);
			for (int i = equalIndex; i <= to; i++) {
				list.swap(storeIndex++, i);
			}
			quickSort(list, storeIndex, to, remaining, comparator);
		}

		private static void heapSort(IntList list, int from, int to, IntComparator comparator) {
			for (int i = (to + from - 1) >> 1; i >= from; i--) {
				siftDown(list, i, to, comparator, from);
			}
			for (int i = to; i > from; i--) {
				list.swap(from, i);
				siftDown(list, from, i - 1, comparator, from);
			}
		}

		private static void siftDown(IntList list, int start, int end, IntComparator comparator, int delta) {
			int value = list.get(start);
			while (true) {
				int child = ((start - delta) << 1) + 1 + delta;
				if (child > end) {
					return;
				}
				int childValue = list.get(child);
				if (child + 1 <= end) {
					int otherValue = list.get(child + 1);
					if (comparator.compare(otherValue, childValue) > 0) {
						child++;
						childValue = otherValue;
					}
				}
				if (comparator.compare(value, childValue) >= 0) {
					return;
				}
				list.swap(start, child);
				start = child;
			}
		}

		private static void insertionSort(IntList list, int from, int to, IntComparator comparator) {
			for (int i = from + 1; i <= to; i++) {
				int value = list.get(i);
				for (int j = i - 1; j >= from; j--) {
					if (comparator.compare(list.get(j), value) <= 0) {
						break;
					}
					list.swap(j, j + 1);
				}
			}
		}

	}

	static class IntArrayList extends IntAbstractStream implements IntList {
		private int size;
		private int[] data;

		public IntArrayList() {
			this(3);
		}

		public IntArrayList(int capacity) {
			data = new int[capacity];
		}

		public IntArrayList(IntCollection c) {
			this(c.size());
			addAll(c);
		}

		public IntArrayList(IntStream c) {
			this();
			if (c instanceof IntCollection) {
				ensureCapacity(((IntCollection) c).size());
			}
			addAll(c);
		}

		public IntArrayList(IntArrayList c) {
			size = c.size();
			data = c.data.clone();
		}

		public IntArrayList(int[] arr) {
			size = arr.length;
			data = arr.clone();
		}

		public int size() {
			return size;
		}

		public int get(int at) {
			if (at >= size) {
				throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
			}
			return data[at];
		}

		private void ensureCapacity(int capacity) {
			if (data.length >= capacity) {
				return;
			}
			capacity = Math.max(2 * data.length, capacity);
			data = Arrays.copyOf(data, capacity);
		}

		public void addAt(int index, int value) {
			ensureCapacity(size + 1);
			if (index > size || index < 0) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			if (index != size) {
				System.arraycopy(data, index, data, index + 1, size - index);
			}
			data[index] = value;
			size++;
		}

		public void removeAt(int index) {
			if (index >= size || index < 0) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			if (index != size - 1) {
				System.arraycopy(data, index + 1, data, index, size - index - 1);
			}
			size--;
		}

		public void set(int index, int value) {
			if (index >= size) {
				throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
			}
			data[index] = value;
		}

	}

	static interface IntComparator {
		public static final IntComparator DEFAULT = (first, second) -> {
			if (first < second) {
				return -1;
			}
			if (first > second) {
				return 1;
			}
			return 0;
		};

		public int compare(int first, int second);

	}

	static interface IntList extends IntReversableCollection {
		public abstract int get(int index);

		public abstract void set(int index, int value);

		public abstract void addAt(int index, int value);

		public abstract void removeAt(int index);

		default public void swap(int first, int second) {
			if (first == second) {
				return;
			}
			int temp = get(first);
			set(first, get(second));
			set(second, temp);
		}

		default public IntIterator intIterator() {
			return new IntIterator() {
				private int at;
				private boolean removed;

				public int value() {
					if (removed) {
						throw new IllegalStateException();
					}
					return get(at);
				}

				public boolean advance() {
					at++;
					removed = false;
					return isValid();
				}

				public boolean isValid() {
					return !removed && at < size();
				}

				public void remove() {
					removeAt(at);
					at--;
					removed = true;
				}
			};
		}


		default public void add(int value) {
			addAt(size(), value);
		}

		default public IntList sort(IntComparator comparator) {
			Sorter.sort(this, comparator);
			return this;
		}

		default public void inPlaceReverse() {
			for (int i = 0, j = size() - 1; i < j; i++, j--) {
				swap(i, j);
			}
		}

		default IntList unique() {
			int last = Integer.MIN_VALUE;
			IntList result = new IntArrayList();
			int size = size();
			for (int i = 0; i < size; i++) {
				int current = get(i);
				if (current != last) {
					result.add(current);
					last = current;
				}
			}
			return result;
		}

		default public IntList subList(final int from, final int to) {
			return new IntList() {
				private final int shift;
				private final int size;

				{
					if (from < 0 || from > to || to > IntList.this.size()) {
						throw new IndexOutOfBoundsException("from = " + from + ", to = " + to + ", size = " + size());
					}
					shift = from;
					size = to - from;
				}

				public int size() {
					return size;
				}

				public int get(int at) {
					if (at < 0 || at >= size) {
						throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
					}
					return IntList.this.get(at + shift);
				}

				public void addAt(int index, int value) {
					throw new UnsupportedOperationException();
				}

				public void removeAt(int index) {
					throw new UnsupportedOperationException();
				}

				public void set(int at, int value) {
					if (at < 0 || at >= size) {
						throw new IndexOutOfBoundsException("at = " + at + ", size = " + size());
					}
					IntList.this.set(at + shift, value);
				}

				public IntList compute() {
					return new IntArrayList(this);
				}
			};
		}

	}

	static class IntArray extends IntAbstractStream implements IntList {
		private int[] data;

		public IntArray(int[] arr) {
			data = arr;
		}

		public int size() {
			return data.length;
		}

		public int get(int at) {
			return data[at];
		}

		public void addAt(int index, int value) {
			throw new UnsupportedOperationException();
		}

		public void removeAt(int index) {
			throw new UnsupportedOperationException();
		}

		public void set(int index, int value) {
			data[index] = value;
		}

	}

	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}

		public static boolean isWhitespace(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);

		}

	}

	static class IOUtils {
		public static void readIntArrays(InputReader in, int[]... arrays) {
			for (int i = 0; i < arrays[0].length; i++) {
				for (int j = 0; j < arrays.length; j++)
					arrays[j][i] = in.readInt();
			}
		}

	}

	static interface IntReversableCollection extends IntCollection {
	}

	static abstract class IntAbstractStream implements IntStream {

		public String toString() {
			StringBuilder builder = new StringBuilder();
			boolean first = true;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				if (first) {
					first = false;
				} else {
					builder.append(' ');
				}
				builder.append(it.value());
			}
			return builder.toString();
		}


		public boolean equals(Object o) {
			if (!(o instanceof IntStream)) {
				return false;
			}
			IntStream c = (IntStream) o;
			IntIterator it = intIterator();
			IntIterator jt = c.intIterator();
			while (it.isValid() && jt.isValid()) {
				if (it.value() != jt.value()) {
					return false;
				}
				it.advance();
				jt.advance();
			}
			return !it.isValid() && !jt.isValid();
		}


		public int hashCode() {
			int result = 0;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				result *= 31;
				result += it.value();
			}
			return result;
		}

	}

	static interface IntCollection extends IntStream {
		public int size();

		default public boolean isEmpty() {
			return size() == 0;
		}

		default public void add(int value) {
			throw new UnsupportedOperationException();
		}

		default public int[] toArray() {
			int size = size();
			int[] array = new int[size];
			int i = 0;
			for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
				array[i++] = it.value();
			}
			return array;
		}

		default public IntCollection addAll(IntStream values) {
			for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
				add(it.value());
			}
			return this;
		}

	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void printLine(int i) {
			writer.println(i);
		}

	}
}

