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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class Main {

	void solve() {
		n = in.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] = in.nextInt();
		}
		for (int i = 0; i < n; i++) {
			b[i] = in.nextInt();
		}
		for (int i = 0; i < n; i++) {
			c[i] = in.nextInt();
		}
		Arrays.sort(a);
		Arrays.sort(b);
		Arrays.sort(c);
		int nowA = 0;
		int nowB = 0;
		int sum = 0;
		int before = 0;
		int beforeId = n - 1;
		int beforeC = 0;
		int beforeCId = n - 1;
		for (int i = n - 1; i > -1; i--) {
			nowA = a[i];
			for (int j = beforeId; j > -1; j--) {
				if (nowA >= b[j]) {
					break;
				}
				beforeId--;
				nowB = b[j];
				for (int k = beforeCId; k > -1; k--) {
					if (nowB >= c[k]) {
						break;
					}
					beforeCId--;
					beforeC++;
				}
				before += beforeC;
			}
			sum += before;
		}

		out.println(sum);
	}

	// only call
	public static void main(String[] args) {
		new Main().solve();
		out.flush();
	}

	// predefined
	FastScanner in = new FastScanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	int n, m, a, b, c, d, e, f;
	int ret;
	ArrayList<Integer> list = new ArrayList<>();
	ArrayDeque<Integer> q = new ArrayDeque<>();

	// 2D-map
	int H, W;
	final int[] dw = new int[] { 0, 1, 0, -1, 1, 1, -1, -1 };
	final int[] dh = new int[] { 1, 0, -1, 0, 1, -1, 1, -1 };

	boolean inField(int nw, int nh) {
		if (nw < 0 || nw >= W || nh < 0 || nh >= H) {
			return false;
		}
		return true;
	}

	// Yes/No
	static String yesno(boolean f) {
		return yesno(f, "YES", "NO");
	}

	static String yesno(boolean f, String yes, String no) {
		return (f ? yes : no);
	}

	// search
	PriorityQueue<Node> pq = new PriorityQueue<>();

	class Node implements Comparable<Node> {

		double score;

		@Override
		public int compareTo(Node o) {
			return Double.compare(this.score, o.score);
		}
	}

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

		FastScanner(InputStream in) {
			this.in = in;
		}

		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 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());
		}
	}
}