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.Comparator;
import java.util.NoSuchElementException;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) throws IOException {
		new Main().solve();
	}

	private void solve() throws IOException {
		try {
			//			solveA();
			//			solveB();
			solveC();
			//			 solveD();
			//			 solveE();
			//			 solveF();
		} finally {
			if (in != null) {
				in.close();
			}
			if (out != null) {
				out.flush();
				out.close();
			}
		}

	}

	private void solveA() {
		StringBuilder wk1 = new StringBuilder(next());
		StringBuilder wk2 = new StringBuilder(next());

		if (wk1.toString().equals(wk2.reverse().toString())) {
			out.println("YES");
		} else {
			out.println("NO");
		}

	}

	private void solveB() {
		int numN = nextInt();

		int wk = (int) Math.sqrt(numN);

		out.println((int) Math.pow(wk, 2));
	}

	private void solveC() {
		int numN = nextInt();
		Long[] aA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] bA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] cA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);

		Arrays.sort(aA, (x, y) -> Long.compare(x, y));
		Arrays.sort(bA, (x, y) -> Long.compare(x, y));
		Arrays.sort(cA, (x, y) -> Long.compare(x, y));

		long res = 0;
		for (int i = 0; i < bA.length; i++) {
			long bP = bA[i];

			//			int aS = getTargetIndexC3(aA, bP);
			long aS = Arrays.binarySearch(aA, bP, new LowerBoundComparator<Long>());
			if (aS < 0) {
				aS = ~aS;
			}

			//			int cS = getTargetIndexC3(cA, bP);
			long cS = Arrays.binarySearch(cA, bP, new UpperBoundComparator<Long>());
			if (cS < 0) {
				cS = ~cS;
			}
			long resT = aS * (long) (numN - cS);
			res += resT;
		}

		out.println(res);
	}

	/**
	 * 指定した値以上の要素が初めて出現する場所を取得
	 * @author works
	 *
	 * @param <T>
	 */
	class LowerBoundComparator<T extends Comparable<? super T>> implements Comparator<T> {
		public int compare(T o1, T o2) {
			return (o1.compareTo(o2) >= 0) ? 1 : -1;
		}
	}

	/**
	 * 指定した値より大きい要素が初めて出現する場所を取得
	 * @author works
	 *
	 * @param <T>
	 */
	class UpperBoundComparator<T extends Comparable<? super T>> implements Comparator<T> {
		@Override
		public int compare(T o1, T o2) {
			return (o1.compareTo(o2) > 0) ? 1 : -1;
		}
	}

	private void solveC3() {
		int numN = nextInt();
		Long[] aA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] bA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] cA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);

		Arrays.sort(aA, (x, y) -> Long.compare(x, y));
		Arrays.sort(bA, (x, y) -> Long.compare(x, y));
		Arrays.sort(cA, (x, y) -> Long.compare(x, y));

		long res = 0;
		for (int i = 0; i < aA.length; i++) {
			long aP = aA[i];

			int bS = getTargetIndexC3(bA, aP);
			if (bS < 0) {
				continue;
			}
			for (int j = bS; j < bA.length; j++) {
				long bP = bA[j];
				if (aP >= bP) {
					continue;
				}
				int cS = getTargetIndexC3(cA, bP);
				if (cS < 0) {
					continue;
				}
				if (bP >= cA[cS]) {
					cS++;
				}
				res += (cA.length - cS);
			}
		}

		out.println(res);
	}

	private int getTargetIndexC3(Long[] wkArray, long num) {
		int wkIndex = -1;

		Arrays.sort(wkArray);

		int start = 0;
		int end = wkArray.length - 1;
		boolean res = true;
		int previousIndex = -1;
		int currentIndex = (start + end) / 2;
		while (res) {

			currentIndex = (start + end) / 2;
			//前回と同じ場合は探索終了
			if (previousIndex == currentIndex) {
				wkIndex = currentIndex;
				break;
			} else {
				//前回と違う場合はindex入れ替え
				previousIndex = currentIndex;
				//前回と違う場合は探索継続
				if (wkArray[currentIndex] == num) {
					wkIndex = currentIndex;
					res = false;
				} else if (wkArray[currentIndex] > num) {
					end = currentIndex;
				} else if (wkArray[currentIndex] < num) {
					start = currentIndex + 1;
				}
			}

		}
		return wkIndex;
	}

	private void solveC2() {
		int numN = nextInt();
		Long[] aA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] bA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);
		Long[] cA = IntStream.range(0, numN).mapToObj(i -> new Long(nextLong())).toArray(Long[]::new);

		Arrays.sort(aA, (x, y) -> Long.compare(x, y) * -1);
		Arrays.sort(bA, (x, y) -> Long.compare(x, y) * -1);
		Arrays.sort(cA, (x, y) -> Long.compare(x, y) * -1);

		long res = 0;
		for (int i = 0; i < aA.length; i++) {
			long aP = aA[i];
			for (int j = 0; j < bA.length; j++) {
				long bP = bA[j];
				if (aP >= bP) {
					break;
				}
				for (int k = 0; k < cA.length; k++) {
					long cP = cA[k];
					if (bP >= cP) {
						break;
					}
					res++;
				}
			}
		}

		out.println(res);
	}

	private void solveD() {
		int numN = nextInt();

		out.println("");
	}

	private void solveE() {
		int numN = nextInt();

		out.println("");
	}

	private void solveF() {
		int numN = nextInt();

		out.println("");
	}

	private final PrintWriter out = new PrintWriter(System.out);
	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;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

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

	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();
		}
	}
}