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.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            input_iter = LazyLoadAllLines();
            //------------------------------------------------//
            var n = Read<long>();
            //var m = Read<long>();
            //var a = Read<long>();
            //var b = Read<long>();
            //var c = Read<long>();
            //var x = Read<long>();
            //var s = Read();
            var ls = Read<long>(n);
            //List<long> als = new List<long>(), bls = new List<long>();
            //List<List<long>> cls = new List<List<long>>();
            /*for (int i = 0; i < m; ++i)
            {
                als.Add(Read<long>());
                bls.Add(Read<long>());
                cls.Add(Read<long>(bls[i]));
            }*/

            ls.Sort((l, r) => (int)(r - l));


            long cnt = 0;
            for(int i = 0; i < n - 2; ++i)
            {
                var first = ls[i];
                int idx = (int)(n - 1);
                for(int j = i + 1; j < idx; ++j)
                {
                    var second = ls[j];
                    for (;idx > j; --idx)
                    {
                        if (ls[idx] + second > first) break;
                    }
                    cnt += idx - j;
                }
            }

            Console.WriteLine(cnt);
        }

        static IEnumerator<string> input_iter;

        static _T Read<_T>() where _T : struct
        {
            input_iter.MoveNext();
            return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
        }
        static string Read()
        {
            input_iter.MoveNext();
            return input_iter.Current;
        }
        static List<_T> Read<_T>(long num) where _T : struct { return new List<_T>(Enumerate<_T>(num)); }


        static IEnumerable<_T> Enumerate<_T>(long num)
        {
            for (long i = 0; i < num; ++i)
            {
                input_iter.MoveNext();
                yield return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
            }
        }
        static IEnumerator<string> LazyLoadAllLines()
        {
            string line;
            do
            {
                line = Console.ReadLine();
                foreach (var s in line.Split(' '))
                    yield return s;
            } while (line != null);
        }
    }
}