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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.Arrays;
import java.util.function.IntPredicate;

public class Main {
    public static void main(String[] args) {
        int n;
        long[] Ai;
        long[] Bi;
        long[] Ci;

        try (InputScanner is = new InputScanner(System.in)) {
            n = is.ni();
            Ai = is.nla(n);
            Bi = is.nla(n);
            Ci = is.nla(n);
        }

        Arrays.sort(Ai);
        Arrays.sort(Bi);
        Arrays.sort(Ci);

        long result = 0;
        for(long b :Bi){
            //AiでB未満が何個あるか
            long a = countLower(Ai,b);

            //CiでB超過が何個あるか
            long c = countHigher(Ci,b);

            result += a*c;
        }
        System.out.println(result);
    }

    private static int lowerBound(long[] a, long key){
        IntPredicate cond = (int index) -> a[index] > key;
        int low = -1;
        int high = a.length;
        while(high - low > 1){
            int mid = low +(high - low)/2;
            if(cond.test(mid)){
                high = mid;
            }else{
                low = mid;
            }
        }
        return high;
    }
    private static int higherBound(long[] a, long key){
        IntPredicate cond = (int index) -> a[index] < key;
        int low = -1;
        int high = a.length;
        while(high - low > 1){
            int mid = low +(high - low)/2;
            if(!cond.test(mid)){
                high = mid;
            }else{
                low = mid;
            }
        }
        return low;
    }

    private static int countLower(long[] array, long maxVal){
        int i = higherBound(array,maxVal);
        return i+1;
    }
    private static int countHigher(long[] array, long minVal){
        int i = lowerBound(array,minVal);
        return array.length - i;
    }

    //-------------------------------------------------------------------
    public static class InputScanner implements Closeable {
        private final BufferedReader br;
        private String[] element;
        private int elementIndex;

        public InputScanner(InputStream is) {
            this.br = new BufferedReader(new InputStreamReader(is));
        }

        public String next() {
            return this.nextElement();
        }

        //next int
        public int ni() {
            return Integer.parseInt(this.nextElement());
        }

        //next long
        public long li() {
            return Long.parseLong(this.nextElement());
        }

        //next int array
        public int[] nia(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.ni();
            }
            return arr;
        }

        //next int array
        public long[] nla(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.ni();
            }
            return arr;
        }
        private void readLine() {
            try {
                this.element = this.br.readLine().split("\\s");
            } catch (IOException e) {
                e.printStackTrace();
            }
            this.elementIndex = 0;
        }

        private String nextElement() {
            if (!hasElement()) {
                this.readLine();
            }
            return this.element[this.elementIndex++];
        }

        private boolean hasElement() {
            return this.element != null && this.element.length > this.elementIndex;
        }

        @Override
        public void close() {
            if (this.br != null) {
                try {
                    this.br.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }
    }
//-------------------------------------------------------------------
}