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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC077C
{
    class Program
    {

        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[] A = ReadInt();
            int[] B = ReadInt();
            int[] C = ReadInt();
            A = A.OrderBy(x => x).ToArray();
            B = B.OrderBy(x => x).ToArray();
            C = C.OrderBy(x => x).ToArray();

            long[] Bunder = new long[N];
            for (int i = 0; i < N; i++)
            {
                int indexA = binary_search(A, B[i]);
                Bunder[i] = indexA;
                if (i > 0) Bunder[i] += Bunder[i - 1];
            }

            long[] Cunder = new long[N];
            for (int i = 0; i < N; i++)
            {
                int indexB = binary_search(B, C[i]) - 1;
                if (indexB >= 0) Cunder[i] = Bunder[indexB];
            }

            long ans = Cunder.Sum();
            Console.WriteLine(ans);
            Console.ReadKey();
        }


        /// <summary>
        /// 二分探索
        /// </summary>
        /// <param name="sortedNums"></param>
        /// <param name="num"></param>
        /// <param name="left"></param>
        /// <param name="right"></param>
        /// <returns></returns>
        public static int BinarySearch<T>(T[] array, T target) where T : IComparable<T>
        {
            int min = 0;
            int max = array.Length - 1;

            while (true)
            {
                // 範囲内に見つからなかった
                //if (max < min) return max;
                // 範囲内の中央値と比較する
                int mid = min + (max - min) / 2;
                switch (target.CompareTo(array[mid]))
                {
                    case -1:    // 中央値より小さい
                        max = mid - 1;
                        if (max < min) return max;
                        break;
                    case 1:     // 中央値より大きい
                        min = mid + 1;
                        if (max < min) return max;
                        break;
                    case 0:     // 見つかった
                        return mid - 1;
                }
            }
        }

        // index が条件を満たすかどうか
        static public bool isOK(int[] sorterArray, int index, int key)
        {
            if (sorterArray[index] >= key) return true;
            else return false;
        }
        // 汎用的な二分探索のテンプレ
        static public int binary_search(int[] sortedArray, int key)
        {
            int ng = -1; //「index = 0」が条件を満たすこともあるので、初期値は -1
            int ok = (int)sortedArray.Length; // 「index = a.size()-1」が条件を満たさないこともあるので、初期値は a.size()

            /* ok と ng のどちらが大きいかわからないことを考慮 */
            while (Math.Abs(ok - ng) > 1)
            {
                int mid = (ok + ng) / 2;

                if (isOK(sortedArray,mid, key)) ok = mid;
                else ng = mid;
            }
            return ok;
        }

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}