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: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

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

public class Main {
    static int MOD = 1000000007;

    static int C(int n, int r) {
        int num = 1;
        for (int i = 1; i <= r; i++) {
            num = num * (n - i + 1) / i;
        }
        return num;
    }

    public static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static long lcm(long a, long b) {
        long temp;
        long c = a;
        c *= b;
        while ((temp = a % b) != 0) {
            a = b;
            b = temp;
        }
        return (long) (c / b);
    }

    static long f(long n, Map<Long, Long> map) {
        if (n < 2)
            return 1;
        else if (map.containsKey(n)) {
            return map.get(n);
        } else {
            map.put(n, n * f(n - 2, map));
            return map.get(n);
        }

    }

    public static long factorial(long n) {
        return n <= 0 ? 1 : n * factorial(n - 1);
    }

    private static long calcLCM(long val1, long val2) {
        long maxValue = Math.max(val1, val2);
        long minValue = Math.min(val1, val2);
        long val3 = maxValue * minValue;

        if (minValue == 0)
            return maxValue;

        long temp;
        while ((temp = maxValue % minValue) != 0) {
            maxValue = minValue;
            minValue = temp;
        }

        return (long) (val3 / minValue);
    }

    static String nextPermutation(String s) {
        ArrayList<Character> list = new ArrayList<>();
        for (int i = 0; i < s.length(); i++)
            list.add(s.charAt(i));

        int pivotPos = -1;
        char pivot = 0;
        for (int i = list.size() - 2; i >= 0; i--) {
            if (list.get(i) < list.get(i + 1)) {
                pivotPos = i;
                pivot = list.get(i);
                break;
            }
        }

        if (pivotPos == -1 && pivot == 0)
            return "Final";

        int L = pivotPos + 1, R = list.size() - 1;
        int minPos = -1;
        char min = Character.MAX_VALUE;
        for (int i = R; i >= L; i--) {
            if (pivot < list.get(i)) {
                if (list.get(i) < min) {
                    min = list.get(i);
                    minPos = i;
                }
            }
        }

        Collections.swap(list, pivotPos, minPos);
        Collections.sort(list.subList(L, R + 1));

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < list.size(); i++)
            sb.append(list.get(i));

        return sb.toString();

    }

    public List<String> permutation(List<String> list, String target, String ans) {
        if (target.length() <= 1) {
            list.add(ans + target);
        } else {
            for (int i = 0; i < target.length(); i++) {
                permutation(list, target.substring(0, i) + target.substring(i + 1), ans + target.charAt(i));
            }
        }
        return list;
    }
        //探索したいkey以上の一番左のイテレータを返す
    public static int lowerBound(int[] a, int key) {
        if (a[a.length - 1] < key)
            return a.length;
        int lb = 0, ub = a.length - 1, mid;
        do {
            mid = (ub + lb) / 2;
            if (a[mid] < key)
                lb = mid + 1;
            else
                ub = mid;
        } while (lb < ub);
        return ub;
    }

    // 探索したいkeyより大きい一番左のイテレータを返す
    public static int upperBound(int[] a, int key) {
        if (a[a.length - 1] <= key)
            return a.length;
        int lb = 0, ub = a.length - 1, mid;
        do {
            mid = (ub + lb) / 2;
            if (a[mid] <= key)
                lb = mid + 1;
            else
                ub = mid;
        } while (lb < ub);
        return ub;
    }

    public static int count(int[] a, int key) {
        return upperBound(a, key) - lowerBound(a, key);
    }

    public static void quickSort(List<Long> data, int left, int right) {
        if (left >= right)
            return;

        int l = left;
        int r = right;
        long p = data.get((left + right) / 2);
        while (l <= r) {
            while (data.get(l) > p) {
                l++;
            }

            while (data.get(r) < p) {
                r--;
            }
            if (l <= r) {
                long temp = data.get(r);
                data.set(r, data.get(l));
                data.set(l, temp);
                l++;
                r--;
            }
        }

        quickSort(data, left, r);
        quickSort(data, l, right);

        return;

    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        int[] c= new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = fs.nextInt();
        }
        Arrays.sort(a);
        for (int i = 0; i < n; i++) {
            b[i] = fs.nextInt();
        }
        for (int i = 0; i < n; i++) {
            c[i] = fs.nextInt();
        }
        Arrays.sort(c);
        long count = 0;
        for (int i = 0; i < n; i++) {
            int val = b[i];
            long av = lowerBound(a, val);
            long cv = n - upperBound(c, val);
            count += av * cv;
        }
        System.out.println(count);
    }
}