Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

// package atcoder.arc.arc074;

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

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        long[] a = in.nextLongs(3*n);

        long[] maxN = new long[3*n+1];
        {
            long sum = 0;
            Queue<Long> q = new PriorityQueue<>();
            for (int i = 0; i < a.length; i++) {
                q.add(a[i]);
                sum += a[i];
                if (q.size() > n) {
                    sum -= q.poll();
                }
                maxN[i+1] = sum;
            }
        }


        long[] minN = new long[3*n+1];
        {
            long sum = 0;
            Queue<Long> q = new PriorityQueue<>();
            for (int i = a.length-1; i >= 0 ; i--) {
                q.add(-a[i]);
                sum += a[i];
                if (q.size() > n) {
                    sum += q.poll();
                }
                minN[a.length-i] = sum;
            }
        }

        long max = -Long.MAX_VALUE;
        for (int l = 0 ; l <= a.length ; l++) {
            int r = a.length-l;
            if (l >= n && r >= n) {
                max = Math.max(max, maxN[l]-minN[r]);
            }
        }

        out.println(max);
        out.flush();
    }

    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[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        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 double nextDouble() {
            return Double.valueOf(nextToken());
        }

        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));
    }
}