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.util.*;
import java.io.*;
public class Main {
	public static void main(String[] args) {
		Solver solver = new Solver();
		solver.solve();
		solver.exit();
	}

	static 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 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 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();
			}
		}
	}

	static class Solver {
		FastScanner sc = new FastScanner();
		public Solver() { }

		String ns() { return sc.next(); }
		String[] ns(int n) {
			String a[] = new String[n];
			for(int i = 0; i < n; i ++) { a[i] = ns(); }
			return a;
		}
		String[][] ns(int n, int m) {
			String a[][] = new String[n][m];
			for(int i = 0; i < n; i ++) { a[i] = ns(m); }
			return a;
		}
		char[] nc(int n) {
			String str = ns();
			char a[] = new char[str.length()];
			for(int i = 0; i < str.length(); i ++) { a[i] = str.charAt(i); }
			return a;
		}
		char[][] nc(int n, int m) {
			char a[][] = new char[n][m];
			for(int i = 0; i < n; i ++) { a[i] = nc(m); }
			return a;
		}
		boolean[] nb(int n, char t) {
			boolean a[] = new boolean[n];
			char c[] = nc(n);
			for(int i = 0; i < n; i ++) { a[i] = c[i] == t; }
			return a;
		}
		boolean[][] nb(int n, int m, char t) {
			boolean a[][] = new boolean[n][m];
			for(int i = 0; i < n; i ++) { a[i] = nb(m, t); }
			return a;
		}
		int ni() { return (int)sc.nextLong(); }
		int[] ni(int n) {
			int a[] = new int[n];
			for(int i = 0; i < n; i ++) { a[i] = ni(); }
			return a;
		}
		int[][] ni(int n, int m) {
			int a[][] = new int[n][m];
			for(int i = 0; i < n; i ++) { a[i] = ni(m); }
			return a;
		}
		long nl() { return sc.nextLong(); }
		long[] nl(int n) {
			long a[] = new long[n];
			for(int i = 0; i < n; i ++) { a[i] = nl(); }
			return a;
		}
		long[][] nl(int n, int m) {
			long a[][] = new long[n][m];
			for(int i = 0; i < n; i ++) { a[i] = nl(m); }
			return a;
		}

		PrintWriter out = new PrintWriter(System.out);
		PrintWriter err = new PrintWriter(System.err);
		void prt() { out.print(""); }
		void prt(int a) { out.print(a); }
		void prt(long a) { out.print(a); }
		void prt(double a) { out.print(a); }
		void prt(String a) { out.print(a); }
		void prt(char a) { out.print(a); }
		void prtln() { out.println(""); }
		void prtln(int a) { out.println(a); }
		void prtln(long a) { out.println(a); }
		void prtln(double a) { out.println(a); }
		void prtln(String a) { out.println(a); }
		void prtln(char a) { out.println(a); }
		void prtln(int... a) {
			StringBuilder sb = new StringBuilder();
			for(int element : a){ sb.append(element+" "); }
			prtln(sb.toString().trim());
		}
		void prtln(long... a) {
			StringBuilder sb = new StringBuilder();
			for(long element : a){ sb.append(element+" "); }
			prtln(sb.toString().trim());
		}
		void prtln(double... a) {
			StringBuilder sb = new StringBuilder();
			for(double element : a){ sb.append(element+" "); }
			prtln(sb.toString().trim());
		}
		void prtln(String... a) {
			StringBuilder sb = new StringBuilder();
			for(String element : a){ sb.append(element+" "); }
			prtln(sb.toString().trim());
		}
		void prtln(char... a) {
			StringBuilder sb = new StringBuilder();
			for(char element : a){ sb.append(element); }
			prtln(sb.toString().trim());
		}
		void prtln(int[][] a) { for(int[] element : a){ prtln(element); } }
		void prtln(long[][] a) { for(long[] element : a){ prtln(element); } }
		void prtln(double[][] a) { for(double[] element : a){ prtln(element); } }
		void prtln(String[][] a) { for(String[] element : a){ prtln(element); } }
		void prtln(char[][] a) { for(char[] element : a){ prtln(element); } }
		void errprt() { err.print(""); }
		void errprt(int a) { err.print(a); }
		void errprt(long a) { err.print(a); }
		void errprt(double a) { err.print(a); }
		void errprt(String a) { err.print(a); }
		void errprt(char a) { err.print(a); }
		void errprt(boolean a) { errprt(a ? "#" : "."); }
		void errprtln() { err.println(""); }
		void errprtln(int a) { err.println(a); }
		void errprtln(long a) { err.println(a); }
		void errprtln(double a) { err.println(a); }
		void errprtln(String a) { err.println(a); }
		void errprtln(char a) { err.println(a); }
		void errprtln(boolean a) { errprtln(a ? "#" : "."); }
		void errprtln(int... a) {
			StringBuilder sb = new StringBuilder();
			for(int element : a){ sb.append(element+" "); }
			errprtln(sb.toString().trim());
		}
		void errprtln(long... a) {
			StringBuilder sb = new StringBuilder();
			for(long element : a){ sb.append(element+" "); }
			errprtln(sb.toString().trim());
		}
		void errprtln(double... a) {
			StringBuilder sb = new StringBuilder();
			for(double element : a){ sb.append(element+" "); }
			errprtln(sb.toString().trim());
		}
		void errprtln(String... a) {
			StringBuilder sb = new StringBuilder();
			for(String element : a){ sb.append(element+" "); }
			errprtln(sb.toString().trim());
		}
		void errprtln(char... a) {
			StringBuilder sb = new StringBuilder();
			for(char element : a){ sb.append(element); }
			errprtln(sb.toString().trim());
		}
		void errprtln(boolean... a) {
			StringBuilder sb = new StringBuilder();
			for(boolean element : a){ sb.append((element ? "#" : ".")+" "); }
			errprtln(sb.toString().trim());
		}
		void errprtln(int[][] a) { for(int[] element : a){ errprtln(element); } }
		void errprtln(long[][] a) { for(long[] element : a){ errprtln(element); } }
		void errprtln(double[][] a) { for(double[] element : a){ errprtln(element); } }
		void errprtln(String[][] a) { for(String[] element : a){ errprtln(element); } }
		void errprtln(char[][] a) { for(char[] element : a){ errprtln(element); } }
		void errprtln(boolean[][] a) { for(boolean[] element : a){ errprtln(element); } }

		void reply(boolean b) { prtln(b ? "Yes" : "No"); }
		void REPLY(boolean b) { prtln(b ? "YES" : "NO"); }

		void exit() { out.flush(); err.flush(); System.exit(0); }

		int min(int a, int b) { return Math.min(a, b); }
		long min(long a, long b) { return Math.min(a, b); }
		double min(double a, double b) { return Math.min(a, b); }
		int min(int... x) {
			int min = x[0];
			for(int val : x) { min = min(min, val); }
			return min;
		}
		long min(long... x) {
			long min = x[0];
			for(long val : x) { min = min(min, val); }
			return min;
		}
		double min(double... x) {
			double min = x[0];
			for(double val : x) { min = min(min, val); }
			return min;
		}
		int max(int a, int b) { return Math.max(a, b); }
		long max(long a, long b) { return Math.max(a, b); }
		double max(double a, double b) { return Math.max(a, b); }
		int max(int... x) {
			int max = x[0];
			for(int val : x) { max = max(max, val); }
			return max;
		}
		long max(long... x) {
			long max = x[0];
			for(long val : x) { max = max(max, val); }
			return max;
		}
		double max(double... x) {
			double max = x[0];
			for(double val : x) { max = max(max, val); }
			return max;
		}
		long sum(int... a) {
			long sum = 0;
			for(int element : a) { sum += element; }
			return sum;
		}
		long sum(long... a) {
			long sum = 0;
			for(long element : a) { sum += element; }
			return sum;
		}
		double sum(double... a) {
			double sum = 0;
			for(double element : a) { sum += element; }
			return sum;
		}

		long abs(double x) { return (long)Math.abs(x); }
		long round(double x) { return Math.round(x); }
		long floor(double x) { return (long)Math.floor(x); }
		long ceil(double x) { return (long)Math.ceil(x); }
		double sqrt(double x) { return Math.sqrt(x); }
		double pow(double x, double y) { return Math.pow(x, y); }
		long pow(long x, long y) { return (long)Math.pow(x, y); }
		int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
		long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
		long lcm(long a, long b) { return a * b / gcd(a, b); }

		long[] div(long a) {
			List<Long> divList = new ArrayList<Long>();
			for(long i = 1; i * i <= a; i ++) {
				if(a % i == 0) {
					divList.add(i);
					if(i * i != a) { divList.add(a / i); };
				}
			}

			long div[] = new long[divList.size()];
			for(int i = 0; i < divList.size(); i ++) { div[i] = divList.get(i); }
			return div;
		}

		long[][] factor(long a) {
			List<Long> factorList = new ArrayList<Long>();
			List<Long> degreeList = new ArrayList<Long>();
			for(long i = 2; i * i <= a; i ++) {
				if(a % i == 0) {
					long count = 0;
					while(a % i == 0) {
						a /= i;
						count ++;
					}
					factorList.add(i);
					degreeList.add(count);
				}
			}
			if(a > 1) {
				factorList.add(a);
				degreeList.add(1L);
			}
			long factor[][] = new long[factorList.size()][2];
			for(int i = 0; i < factorList.size(); i ++) {
				factor[i][0] = factorList.get(i);
				factor[i][1] = degreeList.get(i);
			}
			return factor;
		}

		long[][] countElements(long[] a, boolean sort) {
			int len = a.length;
			long array[] = new long[len];
			for(int i = 0; i < len; i ++) {
				array[i] = a[i];
			}
			if(sort) { Arrays.sort(array); }
			List<Long> elem = new ArrayList<Long>();
			List<Long> cnt = new ArrayList<Long>();
			long tmp = 1;
			for(int i = 1; i <= len; i ++) {
				if(i == len || array[i] != array[i - 1]) {
					elem.add(array[i - 1]);
					cnt.add(tmp);
					tmp = 1;
				}else {
					tmp ++;
				}
			}
			long counts[][] = new long[elem.size()][2];
			for(int i = 0; i < elem.size(); i ++) {
				counts[i][0] = elem.get(i);
				counts[i][1] = cnt.get(i);
			}
			return counts;
		}
		long[][] countElements(String str, boolean sort) {
			int len = str.length();
			char array[] = str.toCharArray();
			if(sort) { Arrays.sort(array); }
			List<Long> elem = new ArrayList<Long>();
			List<Long> cnt = new ArrayList<Long>();
			long tmp = 1;
			for(int i = 1; i <= len; i ++) {
				if(i == len || array[i] != array[i - 1]) {
					elem.add((long)array[i - 1]);
					cnt.add(tmp);
					tmp = 1;
				}else {
					tmp ++;
				}
			}
			long counts[][] = new long[elem.size()][2];
			for(int i = 0; i < elem.size(); i ++) {
				counts[i][0] = elem.get(i);
				counts[i][1] = cnt.get(i);
			}
			return counts;
		}

		int numDigits(long a) { return Long.toString(a).length(); }
		long bitFlag(int a) { return 1L << (long)a; }
		boolean isFlagged(long x, int a) { return (x & bitFlag(a)) != 0; }

		long countString(String str, String a) { return (str.length() - str.replace(a, "").length()) / a.length(); }
		long countStringAll(String str, String a) { return str.length() - str.replaceAll(a, "").length(); }

		void reverse(String array[]) {
			String reversed[] = new String[array.length];
			for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; }
			for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; }
		}
		void reverse(int array[]) {
			int reversed[] = new int[array.length];
			for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; }
			for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; }
		}
		void reverse(long array[]) {
			long reversed[] = new long[array.length];
			for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; }
			for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; }
		}
		void reverse(double array[]) {
			double reversed[] = new double[array.length];
			for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; }
			for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; }
		}
		void reverse(boolean array[]) {
			boolean reversed[] = new boolean[array.length];
			for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; }
			for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; }
		}
		void fill(int array[], int x) { Arrays.fill(array, x); }
		void fill(long array[], long x) { Arrays.fill(array, x); }
		void fill(double array[], double x) { Arrays.fill(array, x); }
		void fill(boolean array[], boolean x) { Arrays.fill(array, x); }
		void fill(int array[][], int x) { for(int a[] : array) { fill(a, x); } }
		void fill(long array[][], long x) { for(long a[] : array) { fill(a, x); } }
		void fill(double array[][], double x) { for(double a[] : array) { fill(a, x); } }
		void fill(boolean array[][], boolean x) { for(boolean a[] : array) { fill(a, x); } }

		long INF = (long)1e+15;
		boolean isINF(long a) { return abs(a) > INF / 1000; }
		boolean isPlusINF(long a) { return a > 0 && isINF(a); }
		boolean isMinusINF(long a) { return isPlusINF(- a); }


		// mods
		long MOD = (long)1e9 + 7; // 998244353;
		public long mod(long i) { return i % MOD + ((i % MOD) < 0 ? MOD : 0); }

		long pow_m(long x, long y) {
			if (y == 0) { return 1;
			}else {
				long tmp = pow_m(x, y / 2);
				return mod(mod(tmp * tmp) * (y % 2 == 0 ? 1 : x));
			}
		}

		long inv(long x) { return pow_m(x, MOD - 2); }

		int MAX_FACT = 5_000_100;
		long fact[];
		long invFact[];
		void prepareFact() {
			fact = new long[MAX_FACT];
			Arrays.fill(fact, 0);
			invFact = new long[MAX_FACT];
			Arrays.fill(invFact, 0);
			fact[0] = 1;
			int maxIndex = min(MAX_FACT, (int)MOD);
			for(int i = 1; i < maxIndex; i ++) { fact[i] = mod(fact[i - 1] * i); }
			invFact[maxIndex - 1] = inv(fact[maxIndex - 1]);
			for(int i = maxIndex - 1; i > 0; i --) { invFact[i - 1] = mod(invFact[i] * i); }
		}

		long P(int n, int r) {
			if(n < 0 || r < 0 || n < r) { return 0; }
			return mod(fact[n] * invFact[n - r]);
		}
		long C(int n, int r) {
			if(n < 0 || r < 0 || n < r) { return 0; }
			return mod(P(n, r) * invFact[r]);
		}
		long H(int n, int r) { return C((n - 1) + r, r); }


		// grid
		class Grid implements Comparable<Grid> {
			int h;
			int w;
			long val;

			Grid() {  }
			Grid(int h, int w) {
				this.h = h;
				this.w = w;
			}
			Grid(int h, int w, long val) {
				this.h = h;
				this.w = w;
				this.val = val;
			}

			@Override
			public int compareTo(Grid g) {
				return Long.compare(this.val, g.val);
			}
		}


		// graph
		class Graph {
			int numNode;
			int numEdge;
			boolean directed;
			Edge edges[];
			Node nodes[];
			Node reversedNodes[];

			Graph(int numNode, int numEdge, Edge edges[], boolean directed) {
				this.numNode = numNode;
				this.numEdge = numEdge;
				this.directed = directed;
				this.edges = edges;
				nodes = new Node[numNode];
				reversedNodes = new Node[numNode];
				for(int i = 0; i < numNode; i ++) {
					nodes[i] = new Node(i);
					reversedNodes[i] = new Node(i);
				}

				for(Edge edge : edges) {
					nodes[edge.source].add(edge.target, edge.cost);
					if(directed) {
						reversedNodes[edge.target].add(edge.source, edge.cost);
					}else {
						nodes[edge.target].add(edge.source, edge.cost);
					}
				}
			}

			void clearNodes() {
				for(Node n : nodes) { n.clear(); }
				for(Node n : reversedNodes) { n.clear(); }
			}
		}

		class Node {
			int id;
			ArrayList<Edge> edges = new ArrayList<Edge>();

			Node(int id) {
				this.id = id;
			}
			void add(int target, long cost) {
				edges.add(new Edge(id, target, cost));
			}
			void clear() {
				edges.clear();
			}
		}

		class Edge implements Comparable<Edge> {
			int source;
			int target;
			long cost;
			Edge(int source, int target, long cost) {
				this.source = source;
				this.target = target;
				this.cost = cost;
			}

			@Override
			public int compareTo(Edge e) {
				return Long.compare(this.cost, e.cost);
			}
		}

public void solve() {
	int num = ni();
	long a[] = nl(num);
	Arrays.sort(a);
	long b[] = nl(num);
	Arrays.sort(b);
	long c[] = nl(num);
	Arrays.sort(c);

	int indexA[] = new int[num];
	for(int i = 0; i < num; i ++) {
		indexA[i] = bisect(b, a[i]);
	}
	long indexB[] = new long[num];
	for(int i = 0; i < num; i ++) {
		indexB[i] = bisect(c, b[i]);
	}

	long sum[] = new long[num + 1];
	sum[num] = 0;
	for(int i = num - 1; i >= 0; i --) {
		sum[i] = sum[i + 1] + (num - indexB[i]);
	}
	long ans = 0;
	for(int i = 0; i < num; i ++) {
		ans += sum[indexA[i]];
	}
	prtln(ans);
}

static int bisect(long array[], long key) {
	int ng = -1;
	int ok = array.length;
	while (Math.abs(ok - ng) > 1) {
		int mid = (ok + ng) / 2;
		if(isOK(array, mid, key)) {
			ok = mid;
		}else {
			ng = mid;
		}
	}
	return ok;
}
static boolean isOK(long array[], int index, long key) { return array[index] > key; }

	}
}