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: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;
 
public class Main implements Runnable {
	
    public static void main(String[] args) {
    	new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
    }
    
    public void run() {
        FastScanner sc = new FastScanner();
        
        int n = sc.nextInt();
        int[] a = sc.nextIntArray(n);
        int[] b = sc.nextIntArray(n);
        int[] c = sc.nextIntArray(n);
        
        Arrays.sort(c);
        Arrays.sort(b);
        
        int[] bs = new int[n];
        
        for(int i=0;i<n;i++){
        	int lb = upperBound(c,b[i]);
        	bs[i] = n-lb;
        }
        
        int[] Cb = cumulativeSumR(bs);
        
        int[] Ca = new int[n];
        
        for(int i=0;i<n;i++){
        	int la = upperBound(b,a[i]);
        	if(la<n){
            	Ca[i] = Cb[la];
        	}
        	else{
        		Ca[i] = 0;
        	}
        }
        
        System.out.println(sum(Ca));
    }
    
	//累積和
	static int[] cumulativeSum(int[] a){
		int[] cs = new int[a.length];
		cs[0] = a[0];
		for(int i=1;i<a.length;i++){
			cs[i] = cs[i-1] + a[i];
		}
		return cs;
	}
	//逆からの累積和
	static int[] cumulativeSumR(int[] a){
		int[] cs = new int[a.length];
		cs[a.length-1] = a[a.length-1];
		for(int i=a.length-2;i>=0;i--){
			cs[i] = cs[i+1] + a[i];
		}
		return cs;
	}
	
	//和
	static long sum(int[] a){
		long sum = 0;
		for(int i:a){
			sum += i;
		}
		return sum;
	}
 
	static int lowerBound(int[] a, int key){
		Integer[] ca = new Integer[a.length];
		
		for(int i=0;i<a.length;i++){
			ca[i] = a[i];
		}
		
		int idx = Arrays.binarySearch(ca, key, (x,y)->x.compareTo(y)>=0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
	//upperBound
	static int upperBound(int[] a, int key){
		Integer[] ca = new Integer[a.length];
		
		for(int i=0;i<a.length;i++){
			ca[i] = a[i];
		}
		
		int idx = Arrays.binarySearch(ca, key, (x,y)->x.compareTo(y)>0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
}


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 int[] nextIntArray(int n){
		int[] a = new int[n];
		for(int i=0;i<n;i++){
			a[i] = nextInt();
		}
		return a;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}