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: Runtime Error)

import java.util.*;
import java.io.*;
public class Main{
  static public class InputIterator{
    ArrayList<String> inputLine = new ArrayList<String>(1024);
    int index = 0; int max;
    InputIterator(){
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      while(true){
        String read;
        try{
          read = br.readLine();
        }catch(IOException e){
          read = null;
        }
        if(read != null){
          inputLine.add(read);
        }else{
          break;
        }
      }
      max = inputLine.size();
    }
    public boolean hasNext(){return (index < max);}
    public String next(){
      if(hasNext()){
        String returnStr = inputLine.get(index);
        index++;
        return returnStr;
      }else{
        throw new IndexOutOfBoundsException("これ以上入力はないよ。");
      }
    }
  }
  
  static InputIterator ii = new InputIterator(); 
  static PrintWriter out = new PrintWriter(System.out);
  static void myout(Object t){out.println(t);}
  static void myerr(Object t){System.err.println(t);}
  static String next(){return ii.next();}
  static int nextInt(){return Integer.parseInt(next());}
  static long nextLong(){return Long.parseLong(next());}
  static ArrayList<String> nextStrArray(){return myHanSpSplit(next());}
  static ArrayList<String> myHanSpSplit(String str){return new ArrayList<String>(Arrays.asList(str.split(" ")));}
  static ArrayList<String> nextCharArray(){return mySingleSplit(next());}
  static ArrayList<String> mySingleSplit(String str){return new ArrayList<String>(Arrays.asList(str.split("")));}
  static ArrayList<Integer> nextIntArray(){
    ArrayList<Integer> ret = new ArrayList<Integer>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Integer.parseInt(input.get(i)));
    }
    return ret;
  }
  static ArrayList<Long> nextLongArray(){
    ArrayList<Long> ret = new ArrayList<Long>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Long.parseLong(input.get(i)));
    }
    return ret;
  }
  static String kaigyoToStr(String[] list){return String.join("\n",list);}
  static String kaigyoToStr(ArrayList<String> list){return String.join("\n",list);}
  static String hanSpToStr(String[] list){return String.join(" ",list);}
  static String hanSpToStr(ArrayList<String> list){return String.join(" ",list);}
  public static void main(String[] args){
    solve();
    out.flush();
  }
  static public void solve(){//ここがメイン関数代わり
    int N = nextInt();
  ArrayList<Integer> alist = nextIntArray();
  Collections.sort(alist);
    ArrayList<Integer> blist = nextIntArray();
  Collections.sort(blist);
    ArrayList<Integer> clist = nextIntArray();
  Collections.sort(clist);
  
  long output = 0;
  for(int i = 0; i < N; i++){
    long tmp = (long)binary_search(alist, blist.get(i), true) * (long)binary_search(clist, blist.get(i), false);
    output += tmp;
  }
  myout(output);
  }
  //Method addition frame start
static public int binary_search(ArrayList<Integer> list,int search,boolean isA){
  //listはあらかじめ昇順ソート済みとする。右側が有効エリア、左側が無効エリアと
  //仮定し、searchによって返す要素(インデックス)は有効な部分の最小値である。
  //逆に無効な部分の最大値を返すなら↑のインデックスを1引いて返せばいい
  int ng = -1;
  int ok = list.size();
  int center;
  while(Math.abs(ok - ng) > 1){
    center = (int)Math.floor((ok + ng) / 2);
    if(list.get(center) >= search){
      ok = center;
    }else{
      ng = center;
    }
  }
  if(isA){
    return ng + 1;
  }else{
    if(list.get(ok) == search){
       ng++;
    }
    return list.size() - (ng + 1);
  }
}
  //Method addition frame end
}