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: Wrong Answer)

'use strict';

const testcase = null;

function main(input) {
    const n = parseInt(input.shift());
    const ls = [];
    const s = new Array(2200).fill(0);
    const m = new Array(2200).fill(0);
    for (var i = 0; i < n; i++) {
        const l = parseInt(input.shift());
        for (var ll of ls) {
            s[l + ll] += 1;
            m[Math.min(l, ll)] += 1;
        }
        ls.push(l);
    }
    for (var i = 0; i < 2100; i++) {
        m[2099 - i] += m[2100 - i];
        s[i + 1] += s[i];
    }
    var total = 0;
    for (var l of ls) {
        //console.log(l, s[l - 1], m[l + 1]);
        total += m[l + 1] - s[l];
    }
    console.log(total);
}

if (process.argv[1] == __filename) {
    const input = testcase
        || require('fs')
            .readFileSync('/dev/stdin', 'utf-8');
    main(input.split(/\s/));
}