Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

// ReSharper disable ArrangeTypeMemberModifiers
// ReSharper disable ConvertIfStatementToSwitchStatement
// ReSharper disable FunctionRecursiveOnAllPaths
// ReSharper disable InconsistentNaming
// ReSharper disable InlineOutVariableDeclaration
// ReSharper disable InvertIf
// ReSharper disable JoinDeclarationAndInitializer
// ReSharper disable MemberCanBeMadeStatic.Global
// ReSharper disable MemberCanBeMadeStatic.Local
// ReSharper disable NonReadonlyMemberInGetHashCode
// ReSharper disable PossibleNullReferenceException
// ReSharper disable RedundantUsingDirective
// ReSharper disable SuggestVarOrType_BuiltInTypes
// ReSharper disable SuggestVarOrType_Elsewhere
// ReSharper disable TailRecursiveCall
// ReSharper disable UnusedMember.Global
// ReSharper disable UnusedMember.Local
// ReSharper disable UseObjectOrCollectionInitializert

#if true && UTAKA_LOCAL

//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;

namespace UtakaApp
{
    public partial class Program
    {
        //=========================================================================================
        // Answer
        //=========================================================================================

        public const string SiteName    = "AtCoder";
        public const string ContestName = "abc143";
        public const string ProblemName = "D";

        public void Solve()
        {
            int   N = cin.ReadInt;
            int[] L = cin.ReadIntArray(N);

            long count = 0;

            Array.Sort(L);

            for (int i = 0; i < N; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    int sum = L[i] + L[j];

                    int k = LowerBound(L, 0, N, sum, Comparer<int>.Default);

                    int distance = N - k;

                    count += (N - 1 - j) - distance;
                }
            }

//            for (int mid = N - 1; mid >= 0; mid--)
//            {
//                for (int low = mid - 1; low >= 0; low--)
//                {
//                    int sum = L[mid] + L[low];
//
//                    int k = LowerBound(L, 0, N, sum, Comparer<int>.Default);
//
//                    int distance = N - k;
//
//                    count += (N - 1 - mid) - distance;
//                }
//            }


//            for (int mid = N - 1; mid >= 0; mid--)
//            {
//                for (int low = mid - 1; low >= 0; low--)
//                {
//                    int sum = L[mid] + L[low];
//
//                    int k = LowerBound(L, 0, N, sum, Comparer<int>.Default);
//
//                    int distance = N - k;
//
//                    count += (N - 1 - mid) - distance;
//
//                }
//            }


//            var comp = new Comp();
//            Array.Sort(L, comp);
//
//            long count = 0;
//
//            for (int i = N - 1; i >= 0; i--)
//            {
//                for (int j = i - 1; j >= 0; j--)
//                {
//                    int sum = L[i] + L[j];
//
//                    int k = UpperBound(L, 0, j, sum, comp);
//
//                    count += (long)Math.Max(0, j - k);
//                }
//            }

            cou.WriteLine(count);
        }

        public class Comp : IComparer<int>
        {
            public int Compare(int x, int y)
            {
                return y - x;
            }
        }

        /// <summary>
        /// 指定した値以上の先頭のインデクスを返します。
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!![exclusive]!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low  = start;
            int high = end;
            while (low < high)
            {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }

            return low;
        }

        /// <summary>
        /// 指定した値以上の先頭のインデクスを返します。
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="value">検索する値</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(T[] arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返します。
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!![exclusive]!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(T[] arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low  = start;
            int high = end;
            while (low < high)
            {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }

            return low;
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返します。
        /// </summary>Z
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="value">検索する値</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(T[] arr, T value)
        {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }

        public class LargeIntComparer : IComparer<int>
        {
            public int Compare(int x, int y)
            {
                return y - x;
            }
        }
    }

//=========================================================================================
// Library
//=========================================================================================


//=========================================================================================
// Debug IO
//=========================================================================================

    public partial class Program
    {
        //=========================================================================================
        // Main
        //=========================================================================================

        private readonly ConsoleInput cin;
        private readonly IConsole     cou;

        public Program(ConsoleInput cin, IConsole cou)
        {
            this.cin = cin;
            this.cou = cou;
        }

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var cin = new ConsoleInput(System.Console.In);
            var console = new MyConsole();
            new Program(cin, console).Solve();
            console.Flush();
#endif
        }
    }

    public class ConsoleInput
    {
        private readonly char          _separator = ' ';
        private readonly TextReader    _stream;
        private readonly Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            _separator  = separator;
            _stream     = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0)
                {
                    return inputStream.Dequeue();
                }

                var tmp = _stream.ReadLine().Split(_separator);
                for (var i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine   => _stream.ReadLine();
        public int    ReadInt    => int.Parse(Read);
        public long   ReadLong   => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);

        public string[] ReadStrArray(long N)
        {
            var ret = new string[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = Read;
            }

            return ret;
        }

        public int[] ReadIntArray(long N)
        {
            var ret = new int[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadInt;
            }

            return ret;
        }

        public long[] ReadLongArray(long N)
        {
            var ret = new long[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadLong;
            }

            return ret;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(object obj);
        void Write(string str);
        void WriteLine(object obj);
        void WriteLine(string str);
        void WriteLine();
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
        }

        public void Flush()
        {
            Console.Out.Flush();
        }

        public void Write(object obj)
        {
            Write(obj.ToString());
        }

        public void Write(string str)
        {
            Console.Write(str);
        }

        public void WriteLine(object obj)
        {
            WriteLine(obj.ToString());
        }

        public void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public void WriteLine()
        {
            Console.WriteLine();
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private readonly StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(object obj)
        {
            Write(obj.ToString());
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(object obj)
        {
            WriteLine(obj.ToString());
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public void WriteLine()
        {
            mSb.AppendLine();
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string GetDirectoryPath()
        {
            var problemPart = string.IsNullOrEmpty(Program.ProblemName)
                ? ""
                : $"/{Program.ProblemName}";

            return
                $"{Environment.GetFolderPath(Environment.SpecialFolder.UserProfile)}/AlgorithmPrac/{Program.SiteName}/{Program.ContestName}{problemPart}";
        }

        private string GetInputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.in";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            return $"{GetDirectoryPath()}/sample-{testCaseNumber}.out";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath  = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);
            var        cin         = new ConsoleInput(inputStream);

            var debugConsoleWriter = new DebugConsole();

            new Program(cin, debugConsoleWriter).Solve();

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var        outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems(int targetTestCaseNumber = -1)
        {
            if (targetTestCaseNumber >= 0)
            {
                Console.WriteLine($"!!!!!!!!!!!! Check TestCase {targetTestCaseNumber} !!!!!!!!!!");
            }

            bool isSuccessAll = true;

            int testCaseNumber = 0;
            while (true)
            {
                testCaseNumber++;

                if (targetTestCaseNumber >= 0 && targetTestCaseNumber != testCaseNumber)
                {
                    continue;
                }

                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    Console.WriteLine("Success");
                }
                else
                {
                    isSuccessAll = false;
                    Console.WriteLine("Failure *****");
                }
            }

            if (isSuccessAll)
            {
                Console.WriteLine("!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}