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: Accepted)

fn main() {
    let n: usize = read_line_as_value();
    let mut v: Vec<usize> = read_line_as_vector();

    v.sort();
    let mut ans = 0;
    for i in 0..n {
        for j in i+1..n {
            let target = v[i] + v[j];
            let mut left = j;
            let mut right = n;
            while right - left > 1 {
                let mid = (left + right) / 2;
                if v[mid] >= target {
                    right = mid;
                } else {
                    left = mid;
                }
            }
            ans += right - 1 - j;
        }
    }
    println!("{}", ans);
}

fn read_line_as_value<T: std::str::FromStr>() -> T {
    let mut input = String::new();
    let res = std::io::stdin().read_line(&mut input);
    if let Err(error) = res {
        panic!("io error at stdin.read_line: {}", error);
    };
    match input.trim().parse() {
        Ok(val) => val,
        _ => panic!("error while parsing input: {}", input)
    }
}

fn read_line_as_vector<T: std::str::FromStr>() -> Vec<T> {
    let mut input = String::new();
    let res = std::io::stdin().read_line(&mut input);
    if let Err(error) = res {
        panic!("io error at stdin.read_line: {}", error);
    };
    match input.trim().split_whitespace().map(|x| x.parse()).collect::<Result<Vec<T>, _>>() {
        Ok(vec) => vec,
        _ => panic!("error while parsing input: {}", input)
    }
}