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)

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

namespace ABC143D
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var l = input.NextInt(n);

            Array.Sort(l);

            var searcher = new SearchOfComparerChangeable<int>();
            long count = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    var min = searcher.UpperBound(l, l[j] - l[i]);
                    var max = searcher.UpperBound(l, l[i] + l[j] - 1);

                    count += Math.Max(0, max - min);

                    if (min <= i && i < max) count--;
                    if (min <= j && j < max) count--;
                }
            }

            Console.WriteLine(count / 3);
        }

        /// <summary>
        /// 二分探索系
        /// 比較処理を外部から注入する用
        /// </summary>
        public class SearchOfComparerChangeable<T>
        {
            /// <summary> 比較用関数 </summary>
            private Comparison<T> Comparison { get; set; }

            public SearchOfComparerChangeable(Comparison<T> comparison = null)
            {
                Comparison = comparison ?? Comparer<T>.Default.Compare;
            }

            /// <summary>
            /// Bound系の下請け
            /// </summary>
            static int FindBound(IList<T> list, T v, int begin, int end, Func<T, T, bool> judge)
            {
                int low = begin, high = end;

                if (low > high)
                {
                    throw new ArgumentException($"{nameof(low)} greater than {nameof(high)}", $"{nameof(low)} and {nameof(high)}");
                }

                while (low < high)
                {
                    var mid = (high + low) / 2;

                    if (judge(v, list[mid])) { high = mid; }
                    else { low = mid + 1; }
                }

                return low;
            }

            /// <summary>
            /// v以上で最小のインデックスを返す
            /// </summary>
            public int LowerBound(IList<T> list, T v, int begin, int end)
                => FindBound(list, v, begin, end, (x, y) => Comparison(x, y) <= 0);

            /// <summary>
            /// v以上で最小のインデックスを返す
            /// </summary>
            public int LowerBound(IList<T> list, T v)
            {
                if (list == null) { throw new ArgumentNullException(nameof(list)); }
                return LowerBound(list, v, 0, list.Count);
            }

            /// <summary>
            /// vより大きな最小のインデックスを返す
            /// </summary>
            public int UpperBound(IList<T> list, T v, int begin, int end)
                => FindBound(list, v, begin, end, (x, y) => Comparison(x, y) < 0);

            /// <summary>
            /// vより大きな最小のインデックスを返す
            /// </summary>
            public int UpperBound(IList<T> list, T v)
            {
                if (list == null) { throw new ArgumentNullException(nameof(list)); }
                return UpperBound(list, v, 0, list.Count);
            }

            /// <summary>
            /// 範囲中でvと等価な個数を返す
            /// </summary>
            public int EqualCount(IList<T> list, T v, int begin, int end)
                => UpperBound(list, v, begin, end) - LowerBound(list, v, begin, end);

            ///// <summary>
            ///// v以下で最大のインデックスを返す
            ///// リストに含まれる最小値より小さな値を指定した場合は-1を返す
            ///// </summary>
            //int OrLess(IList<int> list, int v, int begin, int end)
            //    => new SearchOfComparerChangeable<int>().UpperBound(list, v, begin, end) - 1;

            ///// <summary>
            ///// v未満で最大のインデックスを返す
            ///// リストに含まれる最小値より小さな値を指定した場合は-1を返す
            ///// </summary>
            //int LessThan(IList<T> list, T v, int begin, int end)
            //    => LowerBound(list, v, begin, end) - 1;
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // そのときにTLEするのはアルゴリズムが悪いせいだし、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();

            // 仮想的に標準入力をセットする
            // テスト入力したまま提出することがままあるので……
#if DEBUG
            //input.SetText("5 2 2 2 2 3");
#endif

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path)) { sr = new StreamReader(Console.OpenStandardInput()); }
                else { sr = new StreamReader(path); }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                    SetText(item);
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (string.IsNullOrEmpty(s)) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                    queue.Enqueue(elem);

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any() => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read()) return "";

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                    if (!Read()) return false;

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}