Problem: Mike has always been thinking about the harshness of social inequality. He's so obsessed with it that sometimes it even affects him while solving problems. At the moment, Mike has two sequences of positive integers A = [a1, a2, ..., an] and B = [b1, b2, ..., bn] of length n each which he uses to ask people some quite peculiar questions.

To test you on how good are you at spotting inequality in life, he wants you to find an "unfair" subset of the original sequence. To be more precise, he wants you to select k numbers P = [p1, p2, ..., pk] such that 1 ≤ pi ≤ n for 1 ≤ i ≤ k and elements in P are distinct. Sequence P will represent indices of elements that you'll select from both sequences. He calls such a subset P "unfair" if and only if the following conditions are satisfied: 2·(ap1 + ... + apk) is greater than the sum of all elements from sequence A, and 2·(bp1 + ... + bpk) is greater than the sum of all elements from the sequence B. Also, k should be smaller or equal to <image> because it will be to easy to find sequence P if he allowed you to select too many elements!

Mike guarantees you that a solution will always exist given the conditions described above, so please help him satisfy his curiosity!

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of elements in the sequences. 

On the second line there are n space-separated integers a1, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.

On the third line there are also n space-separated integers b1, ..., bn (1 ≤ bi ≤ 109) — elements of sequence B.

Output

On the first line output an integer k which represents the size of the found subset. k should be less or equal to <image>.

On the next line print k integers p1, p2, ..., pk (1 ≤ pi ≤ n) — the elements of sequence P. You can print the numbers in any order you want. Elements in sequence P should be distinct.

Example

Input

5
8 7 4 8 3
4 2 5 3 7


Output

3
1 4 5

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {
    static FastScanner in;
    static final int MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        //        System.setOut(new PrintStream(new BufferedOutputStream(new FileOutputStream("output.out")), true));
        //        Scanner in = new Scanner(new File("input.txt"));
        //        Scanner in = new Scanner(System.in);
        in = new FastScanner(System.in);
        //        in = new FastScanner("input.txt");
        int n = in.nextInt(), a[] = new int[n], b[] = new int[n];
        boolean flag[] = new boolean[n];
        long sumA = 0, sumB = 0;
        Pair aa[] = new Pair[n], bb[] = new Pair[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            sumA += a[i];
            aa[i] = new Pair(a[i], i);
        }

        for (int i = 0; i < n; i++) {
            b[i] = in.nextInt();
            sumB += b[i];
            bb[i] = new Pair(b[i], i);
        }
        Arrays.sort(aa, new PairComparable());
        Arrays.sort(bb, new PairComparable());
        int p1 = 1;
        Set<Integer> set = new HashSet<Integer>();
        set.add(aa[0].index);
        while (p1 < n - 1) {
            int i1 = aa[p1].index;
            int i2 = aa[++p1].index;
            if (b[i1] > b[i2]) {
                set.add(i1);
            } else {
                set.add(i2);
            }
            p1++;
        }
        if (p1 == n - 1) {
            set.add(aa[p1].index);
        }
        System.out.println(set.size());
        for (int num : set) {
            System.out.print((num + 1) + " ");
        }
    }
}

class Pair {
    Integer val;
    int index;

    public Pair() {
    }

    public Pair(int val, int index) {
        this.val = val;
        this.index = index;
    }
}

class PairComparable implements Comparator<Pair> {
    @Override
    public int compare(Pair o1, Pair o2) {
        return -o1.val.compareTo(o2.val);
    }
}

class FastScanner {

    BufferedReader br;
    StringTokenizer tokenizer;

    FastScanner(String fileName) throws FileNotFoundException {
        this(new FileInputStream(new File(fileName)));
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
    }

    String nextLine() throws IOException {
        tokenizer = null;
        return br.readLine();
    }

    String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }
}