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.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;

class Procon {
    static void Main (string[] agrs) {
        int N = Int ();
        int[] L = Ints ();

        Array.Sort (L);

        long ret = 0;
        for (int i = 0; i < N; i++) {
            for (int j = i + 1; j < N; j++) {
                int max = BinarySearch (L, L[i] + L[j]);
                int min = Math.Max (i, j);

                if (max - min - 1 > 0) {
                    ret += max - min - 1;
                }
            }
        }

        Console.WriteLine (ret);
    }

    static int BinarySearch (int[] a, int b) {
        int index = Array.BinarySearch (a, b);
        if (index < 0) {
            return ~index;
        }
        int tmp = a[index];
        while (tmp == a[index - 1]) {
            index--;
        }

        return index;
    }

    static string String () => Scanner.nextString ();
    static int Int () => int.Parse (Scanner.nextString ());
    static long Long () => long.Parse (Scanner.nextString ());
    static double Double () => double.Parse (Scanner.nextString ());
    static char[] Chars () => String ().ToCharArray ();
    static string[] Strings () => Console.ReadLine ().Split (' ');
    static int[] Ints () => Strings ().Select (v => int.Parse (v)).ToArray ();
    static long[] Longs () => Strings ().Select (v => long.Parse (v)).ToArray ();
    static double[] Doubles () => Strings ().Select (v => double.Parse (v)).ToArray ();
    const int M = 1000000007;
}

class PriorityQueue<T> where T : IComparable<T> {
    public T[] heap;
    public int size;
    public int sign;
    public PriorityQueue (int N, bool descend = false) {
        heap = new T[N];
        sign = 1;
        if (descend) sign = -1;
    }
    public int Compare (T x, T y) {
        return x.CompareTo (y) * sign;
    }
    public void Push (T x) {
        int i = size++;
        while (i > 0) {
            int p = (i - 1) / 2;
            if (Compare (x, heap[p]) >= 0) {
                break;
            }
            heap[i] = heap[p];
            i = p;
        }
        heap[i] = x;
    }
    public T Pop () {
        T ret = heap[0];
        T x = heap[--size];
        int i = 0;
        while (i * 2 + 1 < size) {
            int a = i * 2 + 1;
            int b = i * 2 + 2;
            if (b < size && Compare (heap[a], heap[b]) > 0) {
                a = b;
            }
            if (Compare (heap[a], x) >= 0) {
                break;
            }
            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        return ret;
    }
    public int Count () {
        return size;
    }
}

class Scanner {
    static string[] s = new string[0];
    static int i = 0;
    static int max_i = 0;
    static public string nextString () {
        if (i >= s.Length) {
            s = Console.ReadLine ().Split (' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0) {
                return "";
            }
            return s[i++];
        }
        return s[i++];
    }
}