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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use proconio::{input, fastout};
#[fastout]
fn main() {
    input!{
        n: usize,
        l: [usize;n],
    }

    let mut cnt = 0;
    for i in 0..n-2 {
        for j in i+1..n-1 {
            for k in j+1..n {
                if l[i] < l[j]+l[k] && l[j] < l[k]+l[i] && l[k] < l[i]+l[j] {
                    cnt += 1;
                }
            }
        }
    }
    println!("{}", cnt);
}