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::{fastout, input};
use itertools::Itertools;

#[fastout]
fn main() {
    input! {
        n: usize,
        l: [usize; n],
    }
    let ans = l.iter()
        .combinations(3)
        .filter(|c| meet_condition(c))
        .count();
    println!("{}", ans);
        
}

fn meet_condition(c: &Vec<&usize>) -> bool {
    let a = c[0];
    let b = c[1];
    let c = c[2];
    return  a < &(b + c) && b < &(c + a) && c < &(a + b);
}