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 itertools::Itertools;
use proconio::input;
fn main() {
    input! {
        n: usize,
        l: [usize; n]
    }
    let mut res = 0;
    for i in (0..n).combinations(3) {
        if is_triangle(l[i[0]], l[i[1]], l[i[2]]) {
            res += 1;
        }
    }
    println!("{}", res);
}

fn is_triangle(a: usize, b: usize, c: usize) -> bool {
    if b + c <= a {
        return false;
    }

    if a + c <= b {
        return false;
    }

    if a + b <= c {
        return false;
    }

    true
}