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.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
    public void Solve()
    {
        var N = Int1;
        var L = Ints;
        Array.Sort(L);
        //2*Max(a,b,c)<Sum(a,b,c)
        long ans = 0;
        for (int i = 0; i < N; ++i)
        {
            for (int j = i + 1; j < N; ++j)
            {
                var a = L[i] + L[j];
                ans += BinarySearch.Lower_Bound(L, a, (_, __) => (_ - __)) - j - 1;
            }
        }
        Write(ans);
    }

}


public static class BinarySearch
{
    public static int Lower_Bound<T>(T[] Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1; //always ng
        var r = Array.Length; //always ok
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res >= 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static int Upper_Bound<T>(T[] Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1;
        var r = Array.Length;
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res > 0) r = mid;
            else l = mid;
        }
        return r;
    }
}

public static class Math2
{
    public const int INF = 1 << 29;
    public const long INFL = 1L << 60;
    public const int MOD = 1000000007;
    public const int MOD2 = 998244353;

    public static long Pow(long i, long N, long MOD = 1000000007)
    {
        long res = 1;
        while (N > 0)
        {
            if ((N & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            N >>= 1;
        }
        return res;
    }
    public static long GCD(long i, long N)
    {
        if (i > N) Swap(ref i, ref N);
        if (i == 0) return N;
        while (N != 0)
        {
            var r = i % N;
            i = N;
            N = r;
        }
        return i;
    }
    public static long LCM(long i, long N) => i * N / GCD(i, N);
    public static long Comb(long N, long R, int MOD = 1000000007)
    {
        long ret = 1;
        long x = 1;
        for (long i = N; i >= N - R + 1; --i)
        {
            ret = ret / x * i;
            ret %= MOD;
            x++;
        }
        return ret;
    }
    public static long Comb2(long N, long R)
    {
        long Nume = 1;
        long Deno = 1;

        if (R > N - R) Swap(ref N, ref R);
        for (long i = 1; i <= R; ++i)
        {
            Deno *= i;
            Nume *= N - i + 1;
        }
        return Deno / Nume;
    }
    public static Dictionary<long, int> PrimeFactorization(long N)
    {
        var ret = new Dictionary<long, int>();
        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;
        }
        if (N >= 2) ret[N] = 1;
        return ret;
    }
    public static List<long> DivisorEnumrate(long N)
    {
        var ret = new List<long>();
        for (long i = 1; i * i <= N; ++i)
        {
            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }
        }
        return ret;
    }
}
public static class Utils
{
    public static void Swap<T>(ref T A, ref T B)
    {
        T x = A;
        A = B;
        B = x;
    }
    public static int DigitSum(int N)
    {
        string s = N.ToString();
        int ret = 0;
        for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
        return ret;
    }
}
class Program
{
    static void Main(string[] args)
    {
        var CompetitiveProgramming = new CompetitiveProgramming();
        CompetitiveProgramming.Solve();
    }
}
public static class io
{
    public static string Str => Console.ReadLine();
    public static string[] Strs => Str.Split(' ');
    public static long[] Longs => Strs.Select(long.Parse).ToArray();
    public static int[] Ints => Strs.Select(int.Parse).ToArray();
    public static char[] Chars => Str.ToArray();
    public static double[] Doubles => Strs.Select(double.Parse).ToArray();
    public static long Long1 => Longs[0];
    public static int Int1 => Ints[0];
    public static char Char1 => Chars[0];
    public static double Double1 => Doubles[0];
    public static long[] HorizontalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
    public static void Write(string a) => Console.WriteLine(a);
    public static void Write(params object[] i) => Write(string.Join(" ", i));
    public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
    public static void Horizontalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
    public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}