Problem:
Score : 300 points

Problem Statement

The season for Snuke Festival has come again this year. First of all, Ringo will perform a ritual to summon Snuke. For the ritual, he needs an altar, which consists of three parts, one in each of the three categories: upper, middle and lower.

He has N parts for each of the three categories. The size of the i-th upper part is A_i, the size of the i-th middle part is B_i, and the size of the i-th lower part is C_i.

To build an altar, the size of the middle part must be strictly greater than that of the upper part, and the size of the lower part must be strictly greater than that of the middle part. On the other hand, any three parts that satisfy these conditions can be combined to form an altar.

How many different altars can Ringo build? Here, two altars are considered different when at least one of the three parts used is different.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9(1\leq i\leq N)

1 \leq B_i \leq 10^9(1\leq i\leq N)

1 \leq C_i \leq 10^9(1\leq i\leq N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N
B_1 ... B_N
C_1 ... C_N

Output

Print the number of different altars that Ringo can build.

Sample Input 1

2
1 5
2 4
3 6

Sample Output 1

3

The following three altars can be built:

Upper: 1-st part, Middle: 1-st part, Lower: 1-st part

Upper: 1-st part, Middle: 1-st part, Lower: 2-nd part

Upper: 1-st part, Middle: 2-nd part, Lower: 2-nd part

Sample Input 2

3
1 1 1
2 2 2
3 3 3

Sample Output 2

27

Sample Input 3

6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288

Sample Output 3

87

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) throws IOException {
        FastReader scan = new FastReader();
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("colorful.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Task solver = new Task();
        //int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }
    static class Task {
        public void solve(int testNumber, FastReader sc, PrintWriter pw){
            int n = sc.nextInt();
            int[][] arr = new int[3][n];for(int i=0;i<3;i++)for(int j =0;j<n;j++)arr[i][j]=sc.nextInt();
            shuffle(arr[0]);shuffle(arr[1]);shuffle(arr[2]);
            Arrays.sort(arr[0]);Arrays.sort(arr[1]);Arrays.sort(arr[2]);
            int[] ans = new int[n];
            int ptr = 0;
            for(int i=0;i<n;i++){
                while(ptr<n&&arr[2][ptr]<=arr[1][i]){
                    ptr++;
                }
                ans[i]=n-ptr;
            }
            int[] pref = new int[n+1];
            for(int i=n-1;i>=0;i--){
                pref[i]=pref[i+1]+ans[i];
            }
            long sum = 0;
            ptr= 0;
            for(int i=0;i<n;i++){
                while(ptr<n&&arr[1][ptr]<=arr[0][i]){
                    ptr++;
                }
                sum+=pref[ptr];
            }
            pw.println(sum);
        }
    }
    static class tup implements Comparable<tup> {
        String a, b,c,d;
        tup() {
        }
        ;
        tup(String a,String b,String c,String d) {
            this.a=a;
            this.b=b;
            this.c=c;
            this.d=d;
        }
        @Override
        public int compareTo(tup o2) {
            return 0;
        }
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a,int l, int rb) {
        Random get = new Random();
        for (int i = l; i < rb; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
            public FastReader(String s) throws FileNotFoundException {
                br = new BufferedReader(new FileReader(new File(s)));
            }

            String next() {
                while (st == null || !st.hasMoreElements()) {
                    try {
                        st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                }
                return st.nextToken();
            }

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

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

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

            String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                } catch (IOException e) { e.printStackTrace();
                }return str;
        }
    }
}