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)

input = require('fs').readFileSync('/dev/stdin', 'utf8')
lines = input.split('\n')
N = lines.shift() * 1
line = lines.shift().split(' ')
line.sort((a, b) => b - a)
cnt=0
for (i=0; i<line.length - 2; i++) {
    a = line[i] * 1
    for (j=i+1; j<line.length - 1; j++) {
        b = line[j] * 1
        for (k=j+1; k<line.length; k++) {
            c = line[k] * 1
            if (
                a < b + c &&
                b < c + a &&
                c < a + b
            ) {
                cnt++
            } else {
                break;
            }
        }
    }
}

console.log(cnt)