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 (1.15.1) (judge verdict: Time Limit Exceeded)

fn triangles() -> Result<u32, &'static str> {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;
    let n = input.trim_right().parse::<usize>()
        .map_err(|_| "parse error")?;

    let mut ln = vec![0; n];

    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;
    let l_vec: Vec<&str> = input.split_whitespace().collect();
   
    for i in 0..n {
        ln[i] = l_vec[i].parse::<u32>()
            .map_err(|_| "parse error")?;
    }

    let mut count = 0u32;

    for l1 in 0..(n-2) {

        let a = ln[l1];

        for l2 in (l1+1)..(n-1) {

            let b = ln[l2];

            for l3 in (l2+1)..n {

                let c = ln[l3];

                if a < b + c && b < c + a && c < a + b {
                    count += 1;
                }
            }
        }
    }
    Ok(count)
}

fn main() {
    println!("{}", triangles().unwrap());
}