Problem: You are given two multisets A and B. Each multiset has exactly n integers each between 1 and n inclusive. Multisets may contain multiple copies of the same number.

You would like to find a nonempty subset of A and a nonempty subset of B such that the sum of elements in these subsets are equal. Subsets are also multisets, i.e. they can contain elements with equal values.

If no solution exists, print  - 1. Otherwise, print the indices of elements in any such subsets of A and B that have the same sum.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1 000 000) — the size of both multisets.

The second line contains n integers, denoting the elements of A. Each element will be between 1 and n inclusive.

The third line contains n integers, denoting the elements of B. Each element will be between 1 and n inclusive.

Output

If there is no solution, print a single integer  - 1. Otherwise, your solution should be printed on four lines.

The first line should contain a single integer ka, the size of the corresponding subset of A. The second line should contain ka distinct integers, the indices of the subset of A.

The third line should contain a single integer kb, the size of the corresponding subset of B. The fourth line should contain kb distinct integers, the indices of the subset of B.

Elements in both sets are numbered from 1 to n. If there are multiple possible solutions, print any of them.

Examples

Input

10
10 10 10 10 10 10 10 10 10 10
10 9 8 7 6 5 4 3 2 1


Output

1
2
3
5 8 10


Input

5
4 4 3 3 3
2 2 2 2 5


Output

2
2 3
2
3 5

Solution (in JAVA):

Solution:
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.Random;
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);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskF {
		public void solve(int testNumber, InputReader in, OutputWriter out) {
			int n = in.readInt();
			int[] a = IOUtils.readIntArray(in, n);
			int[] b = IOUtils.readIntArray(in, n);
			int[] aOrder = ArrayUtils.order(a);
			int[] bOrder = ArrayUtils.order(b);
			ArrayUtils.reverse(aOrder);
			ArrayUtils.reverse(bOrder);
			int[] fA = new int[n];
			int[] fB = new int[n];
			int[] was = new int[n + 1];
			for (int i = 0; i < n; i++) {
				was[a[i]] = i + 1;
			}
			for (int i = 0; i < n; i++) {
				if (was[b[i]] != 0) {
					out.printLine(1);
					out.printLine(was[b[i]]);
					out.printLine(1);
					out.printLine(i + 1);
					return;
				}
			}
			Random r = new Random(239);
			for (int j = 0; ; j++) {
				int aSize = 0;
				int bSize = 0;
				int atA = 0;
				int atB = 0;
				int delta = 0;
				int cc = j;
				while (true) {
					if (delta >= 0) {
						if (atA == n) {
							break;
						}
						if (a[aOrder[atA]] == delta) {
							fA[aSize++] = aOrder[atA] + 1;
							print(out, fA, aSize, fB, bSize);
							return;
						}
						if ((cc & 1) != 1) {
							fA[aSize++] = aOrder[atA] + 1;
							delta -= a[aOrder[atA]];
						}
						cc >>= 1;
						atA++;
					} else {
						if (atB == n) {
							break;
						}
						if (b[bOrder[atB]] == -delta) {
							fB[bSize++] = bOrder[atB] + 1;
							print(out, fA, aSize, fB, bSize);
							return;
						}
						if ((cc & 1) != 1) {
							fB[bSize++] = bOrder[atB] + 1;
							delta += b[bOrder[atB]];
						}
						cc >>= 1;
						atB++;
					}
				}
			}
//		out.printLine(-1);
		}

		private void print(OutputWriter out, int[] fA, int aSize, int[] fB, int bSize) {
			Arrays.sort(fA, 0, aSize);
			Arrays.sort(fB, 0, bSize);
			out.printLine(aSize);
			out.printLine(Arrays.copyOf(fA, aSize));
			out.printLine(bSize);
			out.printLine(Arrays.copyOf(fB, bSize));
		}

	}

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

		public void printLine(int[] array) {
			print(array);
			writer.println();
		}

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

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

	}

	static interface IntComparator {
		public int compare(int first, int second);

	}

	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 int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.readInt();
			return array;
		}

	}

	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 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 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 IntReversableCollection extends IntCollection {
	}

	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 Range {
		public static IntList range(int from, int to) {
			int[] result = new int[Math.abs(from - to)];
			int current = from;
			if (from <= to) {
				for (int i = 0; i < result.length; i++) {
					result[i] = current++;
				}
			} else {
				for (int i = 0; i < result.length; i++) {
					result[i] = current--;
				}
			}
			return new IntArray(result);
		}

	}

	static class ArrayUtils {
		public static int[] range(int from, int to) {
			return Range.range(from, to).toArray();
		}

		public static int[] createOrder(int size) {
			return range(0, size);
		}

		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[] order(final int[] array) {
			return sort(createOrder(array.length), new IntComparator() {
				public int compare(int first, int second) {
					if (array[first] < array[second])
						return -1;
					if (array[first] > array[second])
						return 1;
					return 0;
				}
			});
		}

		public static void reverse(int[] array) {
			new IntArray(array).inPlaceReverse();
		}

	}

	static interface IntIterator {
		public int value() throws NoSuchElementException;

		public boolean advance();

		public boolean isValid();

	}
}