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.util.*;
import java.io.*;

public class DoubleKnapscak {
    public static void main(String [] args) {
        Reader in = new Reader ();
        Writer out = new Writer ();
        int n = in.nextInt();
        long [] a = new long [n + 1];
        long [] b = new long [n + 1];

        for(int i = 1; i <= n; i++) {
            a[i] = in.nextInt();
            a[i] += a[i - 1];
        }
        for(int i = 1; i <= n; i++) {
            b[i] = in.nextInt();
            b[i] += b[i - 1];
        }
        boolean rev = (a[n] > b[n]);
        for(int i = 1; i <= n; i++) {
            if(a[n] > b[n]) {
                long tmp = a[i];
                a[i] = b[i];
                b[i] = tmp;
            }
        } 
        int opt[] = new int [n + 1];
        int last[] = new int [n + 1];
        Arrays.fill(last, -1);

        int pt = 0;
        ArrayList <Integer> arr[] = new ArrayList [2];
        arr[0] = new ArrayList <> ();
        arr[1] = new ArrayList <> ();

        for(int i = 0; i <= n; i++) {
            while(pt <= n && b[pt] <= a[i]) {
                ++pt;
            }
            opt[i] = pt - 1;
            int dif = (int)(a[i] - b[opt[i]]);
            if(last[dif] == -1) {
                last[dif] = i;
            } else {
                for(int x = last[dif] + 1; x <= i; x++) {
                    arr[0].add(x);
                }
                for(int x = opt[last[dif]] + 1; x <= opt[i]; x++) {
                    arr[1].add(x);
                }
                break;
            }
        }
        int cur = rev ? 1 : 0;
        for(int i = 0; i < 2; i++) {
            out.writeln(arr[cur].size());
            for(Integer j : arr[cur]) {
                out.write(j + " ");
            }
            out.writeln("");
            cur ^= 1;
        }
        out.flush();
    }
    static class Reader {
        private StringTokenizer a;
        private BufferedReader b;
        Reader () {
            a = null;
            b = new BufferedReader (new InputStreamReader (System.in));
        }
        public String next () {
            while(a == null || !a.hasMoreTokens()) {
                try {
                    a = new StringTokenizer (b.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return a.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(this.next());
        }
        public long nextLong () {
            return Long.parseLong(this.next());
        }
        public double nextDouble () {
            return Double.parseDouble(this.next());
        }
        public String nextLine() {
            try {
                return b.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return "";
        }
    }
    static class Writer {
        private PrintWriter a;
        private StringBuffer b;
        Writer () {
            a = new PrintWriter (System.out);
            b = new StringBuffer ("");
        }
        public void write (Object s) {
            b.append(s);
        }
        public void writeln(Object s) {
            b.append(s).append('\n');
        }
        public void flush () {
            a.print(b);
            a.flush();
            a.close();
        }
    }
    static class Pair implements Comparator <Pair> {
        int first;
        int second;
        Pair  (int a, int b) {
            this.first = a;
            this.second = b;
        }
        Pair (Pair a) {
            this.first = a.first;
            this.second = a.second;
        } 
        Pair () {}
        public String toString () {
            return "[" + first + ", " + second + "]";
        }
        public int compare (Pair a, Pair b) {
            if(a.first == b.first) {
                return a.second - b.second;
            } else {
                return a.first - b.first;
            }
        }
    } 
}