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:
// package codeforces.other2016.wunderfund2016;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * Created by hama_du on 2016/01/30.
 */
public class F {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        long[] a = new long[n];
        long[] b = new long[n];
        for (int i = 0; i < n ; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < n ; i++) {
            b[i] = in.nextInt();
        }
        long sumA = 0;
        long sumB = 0;
        for (int i = 0; i < n ; i++) {
            sumA += a[i];
            sumB += b[i];
        }
        int[] segments = sumA <= sumB ? solve(a, b) : solve(b, a);
        int fromA = segments[0];
        int toA = segments[1];
        int fromB = segments[2];
        int toB = segments[3];
        if (sumA > sumB) {
            fromA = segments[2];
            toA = segments[3];
            fromB = segments[0];
            toB = segments[1];
        }

        String lineA = buildIntegers(fromA, toA);
        String lineB = buildIntegers(fromB, toB);

        out.println(toA - fromA + 1);
        out.println(lineA);
        out.println(toB - fromB + 1);
        out.println(lineB);
        out.flush();
    }

    private static int[] solve(long[] a, long[] b) {
        int[] diffA = new int[1000010];
        int[] diffB = new int[1000010];
        Arrays.fill(diffA, -2);
        Arrays.fill(diffB, -2);
        diffA[0] = -1;
        diffB[0] = -1;

        int n = a.length;
        int fromA = -1;
        int toA = -1;
        int fromB = -1;
        int toB = -1;
        int bi = 0;
        long asum = 0, bsum = 0;
        for (int i = 0 ; i < n ; i++) {
            asum += a[i];
            while (bi < n && bsum + b[bi] <= asum) {
                bsum += b[bi];
                bi++;
            }
            int d = (int)(asum - bsum);
            if (diffA[d] != -2) {
                fromA = diffA[d]+1;
                toA = i;
                fromB = diffB[d]+1;
                toB = bi-1;
                break;
            }
            diffA[d] = i;
            diffB[d] = bi-1;
        }
        return new int[]{fromA, toA, fromB, toB};

    }

    private static String buildIntegers(int fromA, int toA) {
        StringBuilder line = new StringBuilder();
        for (int i = fromA ; i <= toA ; i++) {
            line.append(' ').append(i+1);
        }
        return line.substring(1);
    }

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

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

        private int next() {
            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 char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

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

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

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

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}