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::cmp::{max, min};
use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let mut ll = (0..n).map(|_| read::<usize>()).collect::<Vec<_>>();
    ll.sort();

    let mut ans = 0;
    for ai in 0..n - 2 {
        for ci in ai + 2..n {
            let a = ll[ai] as i64;
            let c = ll[ci] as i64;

            let lower_b = max(a - c + 1, c - a + 1) as usize;
            let upper_b = (a + c - 1) as usize;

            if lower_b <= upper_b {
                let d = ll.binary_search(&lower_b).unwrap_or_else(|x| x);
                let u = ll.binary_search(&upper_b).unwrap_or_else(|x| x);
                let down = max(d, ai + 1);
                let up = min(u, ci - 1);
                if up >= down {
                    ans += up - down + 1
                }
            }
        }
    }
    println!("{}", ans)
}