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: Time Limit Exceeded)

using System.Linq;
class ABC143D
{
    static void Main()
    {
        var number=int.Parse(System.Console.ReadLine());
        var lines=System.Console.ReadLine().Split(' ').Select(
            value=>
            int.Parse(value)
        ).ToArray();
        var counter=0;
        for(int cnt1=0;cnt1<number-2;cnt1++)
        {
            for(int cnt2=cnt1+1;cnt2<number-1;cnt2++)
            {
                counter+=lines
                    .Skip(cnt2+1)
                    .Count(
                        length=>
                        lines[cnt1]+lines[cnt2]>length
                        &&lines[cnt2]+length>lines[cnt1]
                        &&length+lines[cnt1]>lines[cnt2]
                    );
            }
        }
        System.Console.WriteLine(counter);
    }
}