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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function Main(input) {
    input = input.split("\n")
    input = input.map(e=>e.split(" "))
    input = input.map(e=>e.map(f=>parseInt(f,10)))    
    
    var count = 0;
    input[1].forEach((e,i,a)=>{
        var array = a.slice(i+1,a.length);
        var aaa = e
        array.forEach((f,j,b)=>{
            var bray = b.slice(j+1,b.length);
            var bbb = f
            bray.forEach(g=>{                
                if((aaa < bbb + g) && (bbb< g +aaa) && (g<aaa+bbb)){
                    count++;
                }
            })
        })
    })
      
    console.log(count);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));