Problem: Professor GukiZ has two arrays of integers, a and b. Professor wants to make the sum of the elements in the array a sa as close as possible to the sum of the elements in the array b sb. So he wants to minimize the value v = |sa - sb|.

In one operation professor can swap some element from the array a and some element from the array b. For example if the array a is [5, 1, 3, 2, 4] and the array b is [3, 3, 2] professor can swap the element 5 from the array a and the element 2 from the array b and get the new array a [2, 1, 3, 2, 4] and the new array b [3, 3, 5].

Professor doesn't want to make more than two swaps. Find the minimal value v and some sequence of no more than two swaps that will lead to the such value v. Professor makes swaps one by one, each new swap he makes with the new arrays a and b.

Input

The first line contains integer n (1 ≤ n ≤ 2000) — the number of elements in the array a.

The second line contains n integers ai ( - 109 ≤ ai ≤ 109) — the elements of the array a.

The third line contains integer m (1 ≤ m ≤ 2000) — the number of elements in the array b.

The fourth line contains m integers bj ( - 109 ≤ bj ≤ 109) — the elements of the array b.

Output

In the first line print the minimal value v = |sa - sb| that can be got with no more than two swaps.

The second line should contain the number of swaps k (0 ≤ k ≤ 2).

Each of the next k lines should contain two integers xp, yp (1 ≤ xp ≤ n, 1 ≤ yp ≤ m) — the index of the element in the array a and the index of the element in the array b in the p-th swap.

If there are several optimal solutions print any of them. Print the swaps in order the professor did them.

Examples

Input

5
5 4 3 2 1
4
1 1 1 1


Output

1
2
1 1
4 2


Input

5
1 2 3 4 5
1
15


Output

0
0


Input

5
1 2 3 4 5
4
1 2 3 4


Output

1
1
3 1

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Arrays;

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

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.nextIntArray(n);
            int m = in.nextInt();
            int[] b = in.nextIntArray(m);

            long sa = 0, sb = 0;
            for (int i = 0; i < n; ++i) {
                sa += a[i];
            }
            for (int i = 0; i < m; ++i) {
                sb += b[i];
            }

            long bestAnswer = Math.abs(sa - sb);
            int[][] ways = new int[0][];

            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    long newSa = sa - a[i] + b[j];
                    long newSb = sb + a[i] - b[j];
                    if (Math.abs(newSa - newSb) < bestAnswer) {
                        bestAnswer = Math.abs(newSa - newSb);
                        ways = new int[][]{new int[]{i, j}};
                    }
                }
            }

            Record[] index = new Record[m * (m - 1) / 2];
            int last = 0;
            for (int i = 0; i < m; ++i) {
                for (int j = i + 1; j < m; ++j) {
                    index[last++] = new Record(b[i] + b[j], i, j);
                }
            }
            Arrays.sort(index);
            for (int i = 0; i < n && m >= 2; ++i) {
                for (int j = i + 1; j < n; ++j) {
                    long newSa = sa - a[i] - a[j];
                    long newSb = sb + a[i] + a[j];

                    long delta = newSb - newSa;
                    // <= >
                    if (delta > 0) {
                        delta /= 2;
                    } else {
                        delta = -((-delta + 1) / 2);
                    }

                    {
                        int low = 0, high = index.length - 1;
                        while (low < high) {
                            int mid = ((low + high) >> 1) + 1;
                            if (index[mid].sum <= delta) {
                                low = mid;
                            } else {
                                high = mid - 1;
                            }
                        }
                        {
                            newSa += index[low].sum;
                            newSb -= index[low].sum;
                            if (Math.abs(newSa - newSb) < bestAnswer) {
                                bestAnswer = Math.abs(newSa - newSb);
                                ways = new int[][]{new int[]{i, index[low].i},
                                        new int[]{j, index[low].j}};
                            }
                            newSa -= index[low].sum;
                            newSb += index[low].sum;
                        }
                    }


                    {
                        int low = 0, high = index.length - 1;
                        while (low < high) {
                            int mid = (low + high) >> 1;
                            if (index[mid].sum > delta) {
                                high = mid;
                            } else {
                                low = mid + 1;
                            }
                        }
                        {
                            newSa += index[low].sum;
                            newSb -= index[low].sum;
                            if (Math.abs(newSa - newSb) < bestAnswer) {
                                bestAnswer = Math.abs(newSa - newSb);
                                ways = new int[][]{new int[]{i, index[low].i},
                                        new int[]{j, index[low].j}};
                            }
                            newSa -= index[low].sum;
                            newSb += index[low].sum;
                        }
                    }
                }
            }

            out.println(bestAnswer);
            out.println(ways.length);
            for (int[] way : ways) {
                out.println((way[0] + 1) + " " + (way[1] + 1));
            }
        }

        private class Record implements Comparable<Record> {
            long sum;
            int i;
            int j;

            Record(long sum, int i, int j) {
                this.sum = sum;
                this.i = i;
                this.j = j;
            }


            public int compareTo(Record o) {
                return Long.compare(sum, o.sum);
            }

        }

    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new UnknownError();
                }
            }
            return tokenizer.nextToken();
        }

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

        public int[] nextIntArray(int size) {
            int[] result = new int[size];
            for (int i = 0; i < size; ++i) {
                result[i] = nextInt();
            }
            return result;
        }

    }
}