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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ARC077_C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            Treap<int> treapA = new Treap<int>();
            {
                string[] strA = Console.ReadLine().Split(' ');
                for (int i = 0; i < n; ++i)
                {
                    treapA.Insert(int.Parse(strA[i]));
                }
            }

            Treap<int> treapB = new Treap<int>();
            {
                string[] strB = Console.ReadLine().Split(' ');
                for (int i = 0; i < n; ++i)
                {
                    treapB.Insert(int.Parse(strB[i]));
                }
            }

            Treap<int> treapC = new Treap<int>();
            {
                string[] strC = Console.ReadLine().Split(' ');
                for (int i = 0; i < n; ++i)
                {
                    treapC.Insert(int.Parse(strC[i]));
                }
            }

            int[] bigger = new int[n + 1];

            for (int i = n - 1; i >= 0; --i)
            {
                int threshold = treapB[i];

                int findIndex = treapC.FindIndex(threshold);
                if (findIndex == n) { continue; }
                if (treapC[findIndex] == threshold)
                {
                    findIndex = treapC.FindIndex(threshold + 1);
                    //++findIndex;
                }

                if (findIndex == n) { continue; }

                bigger[i] = (n - findIndex) + bigger[i + 1];
            }

            int count = 0;

            for (int i = 0; i < n; ++i)
            {
                int threshold = treapA[i];

                int findIndex = treapB.FindIndex(threshold);
                if (findIndex == n) { break; }
                if (treapB[findIndex] == threshold)
                {
                    findIndex = treapB.FindIndex(threshold + 1);
                    //++findIndex;
                }

                if (findIndex == n) { break; }

                count += bigger[findIndex];
            }

            Console.WriteLine("{0}", count);

            // int findIndex_ = treapC.FindIndex(8);
            // int threshold_ = treapC[findIndex_];
        }

        class Treap<T> where T : IComparable
        {
            private class Node
            {
                private static Random g_rand = new Random();
                private readonly int m_rank = g_rand.Next();
                private readonly T m_value;
                private Node m_lch;
                private Node m_rch;
                private int m_count;

                public Node(T value)
                {
                    m_value = value;
                    m_count = 1;
                }

                public static int Count(Node node)
                {
                    return (node != null) ? node.m_count : 0;
                }

                private Node Update()
                {
                    m_count = Count(m_lch) + Count(m_rch) + 1;
                    return this;
                }

                public static Node Merge(Node a, Node b)
                {
                    if (a == null) { return b; }
                    if (b == null) { return a; }
                    if (a.m_rank < b.m_rank)
                    {
                        a.m_rch = Merge(a.m_rch, b);
                        return a.Update();
                    }
                    else
                    {
                        b.m_lch = Merge(a, b.m_lch);
                        return b.Update();
                    }
                }

                public static Tuple<Node, Node> Split(Node t, int k)
                {
                    if (t == null) { return new Tuple<Node, Node>(null, null); }
                    if (k <= Count(t.m_lch))
                    {
                        var pair = Split(t.m_lch, k);
                        t.m_lch = pair.Item2;
                        return new Tuple<Node, Node>(pair.Item1, t.Update());
                    }
                    else
                    {
                        var pair = Split(t.m_rch, k - Count(t.m_lch) - 1);
                        t.m_rch = pair.Item1;
                        return new Tuple<Node, Node>(t.Update(), pair.Item2);
                    }
                }

                public int FindIndex(T value)
                {
                    int L = Count(m_lch);
                    if (value.CompareTo(m_value) < 0)
                    {
                        return (m_lch != null) ? m_lch.FindIndex(value) : 0;
                    }
                    else if (value.CompareTo(m_value) > 0)
                    {
                        return (m_rch != null) ? m_rch.FindIndex(value) + L + 1 : L + 1;
                    }
                    else
                    {
                        return L;
                    }
                }

                public T this[int i]
                {
                    get
                    {
                        int L = Count(m_lch);
                        if (i < L)
                        {
                            return m_lch[i];
                        }
                        else if (i > L)
                        {
                            return m_rch[i - L - 1];
                        }
                        else
                        {
                            return m_value;
                        }
                    }
                }
            }

            private Node node;

            public void Insert(T value)
            {
                if (node != null)
                {
                    int k = node.FindIndex(value);
                    var pair = Node.Split(node, k);
                    node = Node.Merge(Node.Merge(pair.Item1, new Node(value)), pair.Item2);
                }
                else
                {
                    node = new Node(value);
                }
            }

            public void Erase(T value)
            {
                if (node != null)
                {
                    int k = node.FindIndex(value);
                    var pair = Node.Split(node, k);
                    var pair2 = Node.Split(pair.Item2, 1);
                    node = Node.Merge(pair.Item1, pair2.Item2);
                }
            }

            public int Count()
            {
                return Node.Count(node);
            }

            /// <summary>
            /// 値がvalueなインデックスを返す
            /// valueが無いときは、value以上の値で一番小さいやつのインデックスを返す
            /// valueが全ての値よりも大きい場合は、インデックスはノードの個数を返す。
            /// （存在するインデックスよりもひとつ大きな値（＝ノードの個数の値）を返す）
            /// ※↑のインデックスで、treap[index]として参照しようとすると配列の範囲外アクセスで例外で止まってしまうので注意。
            /// </summary>
            /// <param name="value"></param>
            /// <returns></returns>
            public int FindIndex(T value)
            {
                return node.FindIndex(value);
            }

            public T this[int i]
            {
                get
                {
                    return node[i];
                }
            }
        }

    }
}