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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {
        int itemCount = int.Parse(Reader.ReadLine());

        List<long> partsTop = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).OrderBy(a=>a).ToList();
        List<long> partsMiddle = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).OrderBy(a=>a).ToList();
        List<long> partsBottom = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).OrderBy(a=>a).ToList();
        Dictionary<long, int> newNumDic = new Dictionary<long, int>();
        SortedDictionary<long, bool> numDicWk = new SortedDictionary<long, bool>();
        foreach(List<long> lst in new List<long>[]{partsTop, partsMiddle, partsBottom}) {
            lst.ForEach(a=>{
                numDicWk[a] = true;
            });
        }
        foreach(int key in numDicWk.Keys) {
            newNumDic.Add(key, newNumDic.Count+1);
        }

        int maxNum = (int)newNumDic.Last().Value;

        dic = new Nullable<long>[maxNum + 1];

        List<long>[] tmp = new List<long>[] { partsTop, partsMiddle, partsBottom };
        PartsTopArr = new int[partsTop.Count];
        PartsMiddleArr = new int[partsMiddle.Count];
        PartsBottomArr = new int[partsBottom.Count];

        PartsTopIdx = new int[maxNum + 1];
        PartsTopIdx[0] = -1;
        PartsMiddleIdx = new int[maxNum + 1];
        PartsMiddleIdx[0] = -1;
        PartsBottomIdx = new int[maxNum + 1];
        PartsBottomIdx[0] = -1;

        int[][] tmpArr = new int[][] { this.PartsTopArr, this.PartsMiddleArr, this.PartsBottomArr };
        int[][] tmpIdx = new int[][] { this.PartsTopIdx, this.PartsMiddleIdx, this.PartsBottomIdx };

        for (int i = 0; i < itemCount; i++) {
            for (int j = 0; j < tmp.Length; j++) {
                tmpArr[j][i] = newNumDic[tmp[j][i]];
            }
        }

        for (int i = 1; i <= maxNum; i++) {
            for (int j = 0; j < tmpIdx.Length;j++) {
                int idx = tmpIdx[j][i - 1];
                if(i>=tmpArr[j].Last()) {
                    idx = tmpArr[j].Length;
                } else {
                    while (idx < tmpArr[j].Length - 1 && i >= tmpArr[j][idx + 1])
                    {
                        idx++;
                    }
                }
                tmpIdx[j][i] = idx;
            }
        }
        long ans = 0;
        for (int i = 0; i < PartsTopArr.Length; i++) {
            ans += GetAns(PartsTopArr[i]);
        }
        Console.WriteLine(ans);
    }
    private Nullable<long>[] dic;
    private long GetAns(int top) {
        int midIdx = this.PartsMiddleIdx[top]+1;
        if(midIdx>=this.PartsMiddleArr.Length) {
            return 0;
        }
        if(dic[midIdx]!=null) {
            return dic[midIdx].Value;
        }
        long ans = 0;
        for (int i = midIdx; i < this.PartsMiddleArr.Length; i++) {
            ans += GetAnsSub(PartsMiddleArr[i]);
        }
        dic[midIdx] = ans;
        return ans;
    }

    private long GetAnsSub(int middle) {
        int bottomIdx = PartsBottomIdx[middle] + 1;
        if(bottomIdx>=this.PartsBottomArr.Length) {
            return 0;
        }
        return PartsBottomArr.Length - bottomIdx;
    }

    private int[] PartsTopIdx;
    private int[] PartsMiddleIdx;
    private int[] PartsBottomIdx;

    private int[] PartsTopArr;
    private int[] PartsMiddleArr;
    private int[] PartsBottomArr;

    public class Reader
    {
        private static StringReader sr;
        public static bool IsDebug = false;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (sr == null)
                {
                    sr = new StringReader(InputText.Trim());
                }
                return sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
        private static string InputText = @"



6
3 14 159 2 6 53
58 9 79 323 84 6
2643 383 2 79 50 288


";
    }

    public static void Main(string[] args)
    {
#if DEBUG
        Reader.IsDebug = true;
#endif
        Program prg = new Program();
        prg.Proc();
    }
}