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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static System.Console;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(ReadLine());
        }

        public static long[] Reads()
        {
            return ReadLine().Split().Select(long.Parse).ToArray();
        }

        
         public static long gcd(long x, long y)
        {
            if (x < y) gcd(y, x);
            while (y != 0)
            {
                var z = x;
                x = y;
                y = z % y;
            }
            return x;
        }

        public static long lcm(long x, long y)
        {
            return x * y / gcd(x, y);
        } 

        public static long C(long n, long k)
        {
            long x = 1;
            for (long i = 1; i <= k; i++)
            {
                x *= n - i + 1;
                x /= i;
            }
            return x;
        }

         public static int UpperBound<T>(T[] a, T v)
        {
            return UpperBound(a, v, Comparer<T>.Default);
        }

        public static int UpperBound<T>(T[] a,T v,Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Length - 1;
            while (l <= r)
            {
                var mid = l + (r - 1) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res <= 0) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }

       
        public static int LowerBound(long[] a, long v)
        {
            var l = -1;
            var r = a.Length;
            while (r-l>1)
            {
                var mid = (l + r) / 2;          
                if (a[mid]>=v) r = mid;
                else l = mid;
            }
            return r;
        }


        static void Main(string[] args)
        {
            var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var n = Read();
            var l = Reads();
            Array.Sort(l); 
            long ans = 0;
            for (int i = 0; i < n - 2; i++)
            {
                for (int j = i + 1; j < n-1; j++)
                {
                    ans += LowerBound(l, l[i] + l[j]) - j - 1;
                
                }
            }
           
            WriteLine(ans);

            

            Out.Flush();
        }
    }
}