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: Wrong Answer)

fn input1<T: std::str::FromStr> () -> Result<T, T::Err> {
    let mut n = String::new();
    std::io::stdin().read_line(&mut n).unwrap();
    n.trim().parse()
}

fn input_arr<T: std::str::FromStr> () -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().flat_map(str::parse).collect()
}

fn main() {
    let n: usize = input1().unwrap();
    let mut ls: Vec<usize> = input_arr();
    ls.sort();

    let mut count = 0;
    for i in (1..n).rev() {
        for j in (0..i).rev() {
            let k = ls.binary_search(&(ls[i] + ls[j])).unwrap_or_else(|x| x);
            count += n - (i + 1 + if k > n { k - n } else { n - k });
        }
    }
    println!("{}", count);
}