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)

#![allow(dead_code)]
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let mut l: Vec<usize> = sc.vec(n);
    l.sort_by(|a,b| b.cmp(a));
    let l = l;

    let mut ans = 0;
    for i in 0..l.len() {
        let mut k = l.len()-1;
        for j in i+1..l.len() {
            while l[i]>=l[j]+l[k] { k-=1 }
            if j<k { ans += k-j; }
        }
    }

    format!("{}\n", ans)
}
#[test]
fn test_solve() {
   assert_eq!(solve("4\n3 4 2 1\n"), "1\n");
   assert_eq!(solve("3\n1 1000 1\n"), "0\n");
   assert_eq!(solve("7\n218 786 704 233 645 728 389\n"), "23\n");
}
fn main() {
    let mut buf = String::new();
    use std::io::Read;
    std::io::stdin().read_to_string(&mut buf).unwrap();
    use std::io::Write;
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<I> {
    src: I,
}
impl<'a> Scanner<std::str::SplitWhitespace<'a>> {
    fn from_str(src: &'a str) -> Self {
        Scanner {
            src: src.split_whitespace(),
        }
    }
}
impl<'a, I> Scanner<I>
where
    I: std::iter::Iterator<Item = &'a str>,
{
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.src.next().unwrap().parse().ok().expect("Parse error")
    }
    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    fn chars(&mut self) -> Vec<char> {
        self.src.next().unwrap().chars().collect()
    }
}