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 compareNumbers(a, b) { //for sort
    return b - a;
}

function Main(arg) {
 
    var N = arg.split("\n")[0]-0;
    var L = arg.split("\n")[1].split(" ").map(v=>v-0);
 
    var ans = 0;

    var a, b, c;
    L.sort(compareNumbers);
    for (var i = 0; i < N - 2; i++){
        a = L[i];
        for (var j = i+1; j < N - 1; j++){
            b = L[j];
            for (var t = j+1; t < N; t++){
                c = L[t];
                if (a - b >= c) break;
                if ((a < b + c) && (b < c + a) && (c < a + b)) {
                    ans++;
                }
            }
        }
    }


    console.log(ans)

    return;
}

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