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: Accepted)

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

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn f(u: usize, p: usize, c: u64, edges: &Vec<Vec<(usize, u64)>>, depth: &mut Vec<u64>) {
    depth[u as usize] = c;
    for v in &edges[u] {
        if v.0 == p {
            continue;
        }
        f(v.0, u, c + v.1, edges, depth);
    }
}

fn dist(a: u32, b: u32) -> u32 {
    if a > b {
        a - b
    } else {
        b - a
    }
}

use std::collections::BTreeSet;

fn fun(
    u: usize,
    pvec: &Vec<usize>,
    edges: &Vec<Vec<usize>>,
    vals: &mut BTreeSet<usize>,
    nodes: &mut BTreeSet<usize>,
    checked: &mut BTreeSet<usize>,
) {
    if checked.contains(&u) {
        return;
    }
    checked.insert(u);
    nodes.insert(u);
    vals.insert(pvec[u]);
    for v in &edges[u] {
        fun(*v, pvec, edges, vals, nodes, checked);
    }
}

fn main() {
    let n: usize = read();
    let mut l: Vec<u32> = read_vec();
    l.sort();
    l.push(100000);

    let mut ans: usize = 0;
    for i in 0..n - 2 {
        let mut k = i + 2;
        for j in i + 1..n {
            while l[i] + l[j] > l[k] {
                k += 1;
            }
            ans += k - j - 1;
        }
    }
    println!("{}", ans);
}