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 AC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var L = ReadArrayInt();
            Array.Sort(L);
            var cnt = 0;
            for (int i = 0; i < N - 2; i++)
            {
                for (int j = i + 1; j < N - 1; j++)
                {
                    cnt += LowerBound(L, L[i] + L[j]) - (j + 1);
                }
            }

            Console.WriteLine(cnt);
        }

        static int LowerBound(int[] arr, int val)
        {
            if (arr[0] >= val) return 0;
            if (arr[arr.Length - 1] < val) return arr.Length;

            var low = 0;
            var high = arr.Length - 1;

            while (low + 1 < high)
            {
                var mid = (low + high) / 2;
                if (arr[mid] >= val) high = mid;
                else low = mid;
            }

            return high;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}