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: Time Limit Exceeded)

use std::io::BufRead;
use std::str::FromStr;

fn main() {
    let stdin = std::io::stdin();
    let mut t = Tokenizer::new(stdin.lock().lines().map(|x| x.unwrap()));

    let n: i32 = t.take();
    let mut l: Vec<i32> = Vec::new();
    for _i in 0..n {
        l.push( t.take() );
    }
    let ans = problem( n,l );
    println!("{}",ans);
}

fn problem( n: i32, mut l:  Vec<i32> ) -> i32 {
    l.sort();
    let mut num:i32 = 0;
    for i in 0..n-2 {
        for j in i+1..n-1 {
            for k in j+1..n {
                let (a, b, c) = (l[i as usize], l[j as usize], l[k as usize] );
                if c >= a+b {
                    break;
                }
                if (a < b+c) && (b < a+c) {
                    num += 1;
                }
            }
        }
    }
    num
}

#[cfg(test)]
mod test {
    use super::*;
    #[test]
    fn test1() {
        let result = problem( 4, vec![3,4,2,1] );
        assert_eq!(result,1);
    }
    #[test]
    fn test2() {
        let result = problem( 3, vec![1,1000,1] );
        assert_eq!(result,0);
    }
    #[test]
    fn test3() {
        let result = problem( 7, vec![218,786,704,233,645,728,389] );
        assert_eq!(result,23);
    }
}


struct Tokenizer<S: Iterator<Item = String>> {
    input: S,
    items: Vec<String>,
}

impl<S: Iterator<Item = String>> Tokenizer<S> {
    pub fn new(input: S) -> Self {
        Tokenizer {
            input: input,
            items: Vec::new(),
        }
    }

    pub fn take<T: FromStr>(&mut self) -> T {
        loop {
            if let Some(r) = self.items.pop() {
                return r.parse().ok().expect("parse failed");
            }
            let mut items = self
                .input
                .next()
                .unwrap()
                .split_whitespace()
                .map(|x| x.to_string())
                .collect::<Vec<String>>();
            items.reverse();
            self.items = items;
        }
    }
}