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.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.StringJoiner;

class Main {

    static final int MOD = (int) 1e9 + 7;
    static final int INF = Integer.MAX_VALUE / 2;
    static PrintWriter out;
    static InputReader sc;

    public static void main(String[] args) {
        sc = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    static void solve() {
        int N = sc.nextInt();
        int[] A = sc.nextIntArray(N);
        int[] B = sc.nextIntArray(N);
        int[] C = sc.nextIntArray(N);
        Arrays.sort(A);
        Arrays.sort(B);
        Arrays.sort(C);
        long[] cntB = new long[N];
        long[] sum = new long[N + 1];
        long ans = 0;
        for (int i = 0; i < N; i++) {
            cntB[i] = N - upper_bound(C, B[i]);
        }
        for (int i = N; i > 0; i--) {
            sum[i - 1] = cntB[i - 1];
            sum[i - 1] += sum[i];
        }
        for (int i = 0; i < N; i++) {
            ans += sum[upper_bound(B, A[i])];
        }
        out.println(ans);
    }

    /**
     * ソートされたarr内で、keyより大きい要素の内の一番左側のindexを求める O(log(n))
     *
     * @param arr
     * @param key
     * @return arr内で、keyより大きい要素の内の一番左側のindex
     */
    public static int upper_bound(int[] arr, int key) {
        int low = 0;
        int high = arr.length;
        int mid;
        while (low < high) {
            mid = ((high - low) >>> 1) + low;
            if (arr[mid] <= key) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            Class<?> type = arg.getClass();
            if (!type.isArray()) {
                j.add(arg.toString());
            } else if (type.getComponentType().isArray()) {
                for (Object o : (Object[]) arg) {
                    debug(o);
                }
            } else if (arg instanceof int[]) {
                j.add(Arrays.toString((int[]) arg));
            } else if (arg instanceof long[]) {
                j.add(Arrays.toString((long[]) arg));
            } else if (arg instanceof double[]) {
                j.add(Arrays.toString((double[]) arg));
            } else if (arg instanceof char[]) {
                j.add(Arrays.toString((char[]) arg));
            } else if (arg instanceof boolean[]) {
                j.add(Arrays.toString((boolean[]) arg));
            } else if (arg instanceof Object[]) {
                j.add(Arrays.toString((Object[]) arg));
            } else {
                j.add(arg.toString());
            }
        }
        System.err.println(j.toString());
    }

    static class InputReader {

        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;

        public InputReader(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }

        public boolean hasNextByte() {
            if (this.curbuf >= this.lenbuf) {
                this.curbuf = 0;
                try {
                    this.lenbuf = this.in.read(this.buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (this.lenbuf <= 0) {
                    return false;
                }
            }
            return true;
        }

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

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private void skip() {
            while (this.hasNextByte() && this.isSpaceChar(this.buffer[this.curbuf])) {
                this.curbuf++;
            }
        }

        public boolean hasNext() {
            this.skip();
            return this.hasNextByte();
        }

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

        public int nextInt() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

        public long nextLong() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

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

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = this.nextInt();
            }
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = this.nextLong();
            }
            return a;
        }

        public char[][] nextCharMap(int n, int m) {
            char[][] map = new char[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = this.next().toCharArray();
            }
            return map;
        }
    }
}