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)

use std::str::FromStr;
use std::io::stdin;
use std::iter::FromIterator;

fn main() {
    let n = read::<usize>();
    let mut vec = read_vec::<usize>();
    vec.sort();
    vec.reverse();
    let mut total = 0_usize;
    for i in 0..n {
        for j in (i + 1)..n {
            let mut sub = Vec::from_iter(vec[(j + 1)..n].iter().cloned());
            sub.reverse();
            let len = vec[i] - vec[j] + 1;
            let res = sub.binary_search(&len);
            let idx = match res {
                Ok(x) => x,
                Err(x) => x,
            };
            if sub.len() <= len + 1 {
                total += sub.len() - idx;
            }
        }
    }
    println!("{}", total);
}

fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).ok();
    line.trim().parse().ok().unwrap()
}

fn read_vec<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).ok();
    line.trim().split_whitespace()
        .map(|i| i.parse().ok().unwrap()).collect()
}