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# (.NET Core 3.1.201) (judge verdict: Accepted)


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

    class Program
    {
        static void Main()
        {
            var n = Console.ReadLine().ToInt32();
            var a = System.Console.ReadLine().Split(' ').Select((x) => long.Parse(x)).ToArray();
            var b = System.Console.ReadLine().Split(' ').Select((x) => long.Parse(x)).ToArray();
            var c = System.Console.ReadLine().Split(' ').Select((x) => long.Parse(x)).ToArray();

            Array.Sort(a);
            Array.Sort(b);
            Array.Sort(c);
            long ans = 0;
            for (int i = 0; i < b.Count(); i++)
            {
                var aIdx = LowerBound(a, b[i]) - 1;
                if (aIdx < 0) continue;

                var cIdx = UpperBound(c, b[i]);
                if (cIdx > n - 1) continue;

                //組み合わせ
                long combi = (long)(aIdx + 1) * (long)(n - cIdx);
                ans += combi;
            }
            Output(ans.ToString());

        }
        private static int LowerBound(long[] arr, long target)
        {
            var min = 0;
            var max = arr.Length - 1;

            while (max >= min)
            {
                int mid = min + (max - min) / 2;
                if (arr[mid] < target)
                {
                    min = mid + 1;
                }
                else
                {
                    max = mid - 1;
                }
            }
            //target以上となる最初のインデックスを出力
            return min;
        }
        private static int UpperBound(long[] arr, long target)
        {
            var min = 0;
            var max = arr.Length - 1;

            while (max >= min)
            {
                var mid = (min + max) / 2;
                if (arr[mid] <= target)
                {
                    min = mid + 1;
                }
                else
                {
                    max = mid - 1;
                }
            }
            //target以上となる最初のインデックスを出力
            return min;
        }
        private static void Output(string str)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            Console.WriteLine(str);

            Console.Out.Flush();
        }

    }

    static class Extentions
    {
        #region 拡張メソッド（string）

        public static string LeftB(this string stTarget, int iByteSize)
        {
            return MidB(stTarget, 1, iByteSize);
        }

        public static string MidB(this string stTarget, int iStart)
        {
            System.Text.Encoding hEncoding = System.Text.Encoding.GetEncoding("utf-8");
            byte[] bBytes = hEncoding.GetBytes(stTarget);

            return hEncoding.GetString(bBytes, iStart - 1, bBytes.Length - iStart + 1);
        }

        public static string MidB(this string stTarget, int iStart, int iByteSize)
        {
            System.Text.Encoding hEncoding = System.Text.Encoding.GetEncoding("utf-8");
            byte[] bBytes = hEncoding.GetBytes(stTarget);

            return hEncoding.GetString(bBytes, iStart - 1, iByteSize);
        }

        public static string RightB(this string stTarget, int iByteSize)
        {
            System.Text.Encoding hEncoding = System.Text.Encoding.GetEncoding("utf-8");
            byte[] bBytes = hEncoding.GetBytes(stTarget);

            return hEncoding.GetString(bBytes, bBytes.Length - iByteSize, iByteSize);
        }

        public static bool IsNullOrEmpty(this string str)
        {
            return string.IsNullOrEmpty(str);
        }

        /// <summary>
        /// カルチャに依存した比較、または大文字と小文字を区別しない比較などの序数による比較を指定できる Contains。
        /// </summary>
        /// <param name="value">対象文字列</param>
        /// <param name="partialValue">部分文字列</param>
        /// <param name="comparison">カルチャ、大文字と小文字の区別、および並べ替え規則を指定する StringComparison</param>
        /// <returns>一致する場合に true を返します。</returns>
        public static bool Contains(this string value, string partialValue, StringComparison comparison = 0)
        {
            return value.IndexOf(partialValue, comparison) >= 0;
        }

        public static bool IsNumeric(this string value)
        {
            return decimal.TryParse(value, out decimal d);
        }
        public static int ToInt32(this String number, int retValue = 0)
        {
            if (!number.IsNumeric()) return retValue;
            return int.Parse(number);
        }

        #endregion
    }