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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Reflection.Emit;
using System.Security.Cryptography;
using System.Text;
using System.Threading;
namespace Program{
    class MainClass{
        ////////////////////////////////////////////////////////////
        private int N;
        private int[] A, B, C;
        void Solve(){
            N = io.Int;
            A = io.arrInt;
            B = io.arrInt;
            C = io.arrInt;
            A.Sort();
            B.Sort();
            C.Sort();
            var ans = 0;
            for(int i=0;i<N;++i){
                var abNum = A.LowerBound(B[i]);
                var bcNum = N - C.UpperBound(B[i]);
                ans += abNum * bcNum;
            }
            io.o(ans);
        }

        ////////////////////////////////////////////////////////////
        public static void Main() { new MainClass().Stream(); }
        IO io = new IO();
        Mat mat = new Mat();
        void Stream(){
            Solve();
            //Test();
            io.writeFlush();
        }
        void Test(){
            //var arr = Enumerable.Range(1, 5).ToArray();
            //io.o(arr.UpperBound(4));
        }
        #region MockMacro
        //cannot use break,continue,goto
        void FOR(int a, int b, Action<int> act){
            for(int i = a; i < b; ++i) act(i);
        }
        void FORR(int a, int b, Action<int> act){
            for(int i = a - 1; i >= b; --i) act(i);
        }
        #endregion
        ////////////////////////////////////////////////////////////
    }
    #region default
    class IO{
        string[] nextBuffer;
        int BufferCnt;
        char[] cs = new char[]{' '};
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
        public IO(){
            nextBuffer = new string[0];
            BufferCnt = 0;
            Console.SetOut(sw);
        }
        public string Next(){
            if(BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while(st == "") st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public string String => Next();
        public char Char => char.Parse(String);
        //public int Int => int.Parse(String);
        public int Int => String.toInt();
        public long Long => String.toLong();
        public double Double => double.Parse(String);
        public string[] arr => Console.ReadLine().Split(' ');
        public char[] arrChar => Array.ConvertAll(arr, char.Parse);
        //public int[] arrInt => Array.ConvertAll(arr, int.Parse);
        public int[] arrInt => arr.Select(v => v.toInt()).ToArray();
        //public long[] arrLong => Array.ConvertAll(arr, long.Parse);
        public long[] arrLong => arr.Select(v => v.toLong()).ToArray();
        public double[] arrDouble => Array.ConvertAll(arr, double.Parse);
        public T i<T>() { return suitType<T>(String); }
        public void i<T>(out T v) { v = suitType<T>(String); }
        public void i<T, U>(out T v1, out U v2){
            i(out v1);
            i(out v2);
        }
        public void i<T, U, V>(out T v1, out U v2, out V v3){
            i(out v1);
            i(out v2);
            i(out v3);
        }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4){
            i(out v1);
            i(out v2);
            i(out v3);
            i(out v4);
        }
        public void i<T, U, V, W, X>(out T v1, out U v2, out V v3, out W v4, out X v5){
            i(out v1);
            i(out v2);
            i(out v3);
            i(out v4);
            i(out v5);
        }
        public void ini<T>(out T[] a, int n){
            a = new T[n];
            for(int i = 0; i < n; ++i) a[i] = suitType<T>(String);
        }
        public void ini<T, U>(out T[] a, out U[] b, int n){
            a = new T[n];
            b = new U[n];
            for(int i = 0; i < n; ++i){
                a[i] = i<T>();
                b[i] = i<U>();
            }
        }
        public void ini<T, U, V>(out T[] a, out U[] b, out V[] c, int n){
            a = new T[n];
            b = new U[n];
            c = new V[n];
            for(int i = 0; i < n; ++i){
                a[i] = i<T>();
                b[i] = i<U>();
                c[i] = i<V>();
            }
        }
        public void ini<T, U>(out Tuple<T, U>[] t, int n){
            t = new Tuple<T, U>[n];
            for(int j = 0; j < n; ++j){
                T i1;
                U i2;
                i(out i1);
                i(out i2);
                t[j] = Tuple.Create(i1, i2);
            }
        }
        public void ini<T, U, V>(out Tuple<T, U, V>[] t, int n){
            t = new Tuple<T, U, V>[n];
            for(int j = 0; j < n; ++j){
                T i1;
                U i2;
                V i3;
                i(out i1);
                i(out i2);
                i(out i3);
                t[j] = Tuple.Create(i1, i2, i3);
            }
        }
        public void ini<T>(out T[,] a, int h, int w){
            a = new T[h, w];
            for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) a[i, j] = i<T>();
        }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void o<T>(params T[] a) { Array.ForEach(a, n => o(n)); }
        public void o<T>(T[,] a){
            int a0 = a.GetLength(0), a1 = a.GetLength(1);
            for(int i = 0; i < a0; ++i){
                for(int j = 0; j < a1 - 1; ++j) Console.Write(a[i, j] + " ");
                Console.WriteLine(a[i, a1 - 1]);
            }
        }
        public void YN(bool f) { o(f ? "YES" : "NO"); }
        public void Yn(bool f) { o(f ? "Yes" : "No"); }
        public void yn(bool f) { o(f ? "yes" : "no"); }
        public void ol<T>(params T[] a) { o(connect<T>(a)); }
        public void or<T>(T a) { Console.Write(a); }
        public void br() { o(""); }
        public void writeFlush() { Console.Out.Flush(); }
        private string connect<T>(params T[] s) { return string.Join(" ", s); }
        private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        private T convertType<T, U>(U v) { return (T) Convert.ChangeType(v, typeof(T)); }
        private T suitType<T>(string s){
            if(typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if(typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if(typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if(typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
    }
    class Mat{
        public long mod = 1000000007;//10^9+7
        public long Pow(long a, long b){
            if(b == 0) return 1;
            if(b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n){
            long ret = 1;
            for(long i = 1; i <= n; i++) ret = (ret * i) % mod;
            return ret;
        }
        public long ModC(long n, long r){
            if(r == 0 || n == r) return 1;
            if(n == 0) return 0;
            if(n < 0 || n < r) throw new ArgumentException("n,r invalid");
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long[,] C(int N){
            long[,] Co = new long[N + 1, N + 1];
            (N + 1).REP(i => (i + 1).REP(j => Co[i, j] = (j == 0 || j == i) ? 1L : Co[i - 1, j - 1] + Co[i - 1, j]));
            return Co;
        }
        public long DupC(long n, long r) { return ModC(n + r - 1, r); }
        public long P(long n, long r) { return Fact(n) / (Fact(n - r)); }//test
        public bool isPrime(long n){
            if(n == 2) return true;
            if(n < 2 || n % 2 == 0) return false;
            for(long v = 3; v <= (long) Math.Sqrt(n); v += 2) if(n % v == 0) return false;
            return true;
        }
        public long LCM(long a, long b) { return a * (b / GCD(a, b)); }
        public long LCM(params long[] a) { return a.Aggregate((v, n) => LCM(v, n)); }
        public long GCD(long a, long b){
            if(a < b) Swap(ref a, ref b);
            return b == 0 ? a : GCD(b, a % b);
        }
        public long GCD(params long[] array) { return array.Aggregate((v, n) => GCD(v, n)); }
        public T Max<T>(params T[] a) { return a.Max(); }
        public T Min<T>(params T[] a) { return a.Min(); }
        public void Swap<T>(ref T a, ref T b){
            T tmp = a;
            a = b;
            b = tmp;
        }
        public double Dis(int x1, int y1, int x2, int y2) { return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2)); }
        public int mDis(int x1, int y1, int x2, int y2) { return Math.Abs(x1 - x2) + Math.Abs(y1 - y2); }
        public int[] DigArr(int n){
            int[] ret = new int[Digit(n)];
            ret.Length.REP(i => ret[i] = DigVal(n, i + 1));
            return ret;
        }
        public long DigArr2Num(IEnumerable<int> enu) { return enu.Aggregate((v, n) => v * 10 + n); }
        public int Digit(long n) { return (n == 0) ? 1 : (int) Math.Log10(n) + 1; }
        public int DigVal(int n, int dig) { return (n % (int) Pow(10, dig)) / (int) Pow(10, dig - 1); }
        public long Tousa(long a, long d, long n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, long n) { return n * (2 * a + (n - 1) * d) / 2; }
        public long[] EnuDivsor(long N){
            var ret = new SortedSet<long>();
            for(long i = 1; i * i <= N; i++)
                if(N % i == 0){
                    ret.Add(i);
                    ret.Add(N / i);
                }
            return ret.ToArray();
        }
        public Dictionary<long, long> PrimeFactor(long n){
            var ret = new Dictionary<long, long>();
            for(int i = 2; i * i <= n; ++i){
                if(!ret.ContainsKey(i)) ret[i] = 0;
                while(n % i == 0){
                    ++ret[i];
                    n /= i;
                }
            }
            return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
        }
    }
    #endregion
    #region Ex
    static class StringEX{
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
        public static int toInt(this string s){
            int n;
            return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0;
        }
        public static int toInt(this char c) { return toInt(c.ToString()); }
        public static int toInt(this char[] c) { return toInt(new string(c)); }
        public static long[] toLong(this int[] a) { return a.Select(v => (long) v).ToArray(); }
        public static long[,] toLong(this int[,] m){
            var h = m.GetLength(0);
            var w = m.GetLength(1);
            var ret = new long[h, w];
            for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) ret[i, j] = (long) m[i, j];
            return ret;
        }
        public static long toLong(this string s){
            long n;
            return (long.TryParse(s.TrimStart('0'), out n)) ? n : (long) 0;
        }
        public static long toLong(this char c) { return toLong(c.ToString()); }
        public static long toLong(this char[] c) { return toLong(new string(c)); }
        public static string toString(this char[] c) { return new string(c); }
    }
    static class NumericEx{
        public static string pad0<T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
        public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
        public static double RoundUp(this double v) { return Math.Ceiling(v); }
        public static double RoundDown(this double v) { return Math.Floor(v); }
        public static bool Odd(this int v) { return v % 2 != 0; }
        public static bool Odd(this long v) { return v % 2 != 0; }
        public static void REP(this int v, Action<int> act){
            for(int i = 0; i < v; ++i) act(i);
        }
        public static void REPR(this int v, Action<int> act){
            for(int i = v - 1; i >= 0; --i) act(i);
        }
    }
    static class ArrayEX{
        public static T[] Sort<T>(this T[] a){
            Array.Sort(a);
            return a;
        }
        public static T[] SortR<T>(this T[] a){
            Array.Sort(a);
            Array.Reverse(a);
            return a;
        }
        public static void Set<T>(this T[] a, T v) { a.Length.REP(i => a[i] = v); }
        public static void Set<T>(this T[,] a, T v) { a.GetLength(0).REP(i => a.GetLength(1).REP(j => a[i, j] = v)); }
        public static int[] toIntArr(this string a) { return a.Select(c => c.toInt()).ToArray(); }
        public static int[] toIntArr(this string[] a) { return Array.ConvertAll(a, int.Parse); }
        public static long[] toLongArr(this string a) { return a.Select(c => c.toLong()).ToArray(); }
        public static long[] toLongArr(this string[] a) { return Array.ConvertAll(a, long.Parse); }
        public static double[] toDoubleArr(this string[] a) { return Array.ConvertAll(a, double.Parse); }
        public static char[] toCharArr(this string[] a) { return Array.ConvertAll(a, char.Parse); }
        public static int LowerBound<T>(this T[] a, T x) where T : IComparable{
            Array.Sort(a);
            int lb = -1, ub = a.Length;
            while(ub - lb > 1){
                var mid = (ub + lb) / 2;
                if(a[mid].CompareTo(x) >= 0) ub = mid;
                else lb = mid;
            }
            return ub;
        }
        public static int UpperBound<T>(this T[] a, T x) where T : IComparable{
            Array.Sort(a);
            int lb = -1, ub = a.Length;
            while(ub - lb > 1){
                var mid = (ub + lb) / 2;
                if(a[mid].CompareTo(x) > 0) ub = mid;
                else lb = mid;
            }
            return  ub;
        }
    }
    #endregion
}