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)

use std::io::stdin;
use std::vec::Vec;

mod utils {
    use std::io::BufRead;
    use std::str::{self, FromStr};

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(reader: R) -> StdinReader<R> {
            StdinReader {
                reader: reader,
                buf: Vec::new(),
            }
        }

        #[allow(unused)]
        #[inline]
        pub fn reads<T: FromStr>(&mut self) -> T {
            self.read_until(b' ')
        }

        #[allow(unused)]
        #[inline]
        pub fn readl<T: FromStr>(&mut self) -> T {
            self.read_until(b'\n')
        }

        #[allow(unused)]
        #[inline]
        pub fn read_vec<T: FromStr>(&mut self) -> Vec<T> {
            return self.read_until::<String>(b'\n').trim().split_whitespace().map(|c| c.parse().ok().unwrap()).collect();
        }

        #[inline]
        pub fn read_until<T: FromStr>(&mut self, delim: u8) -> T {
            loop {
                self.buf.clear();
                let len = self.reader
                    .read_until(delim, &mut self.buf)
                    .expect("failed reading bytes");
                match len {
                    0 => panic!("early eof"),
                    1 if self.buf[0] == delim => (),
                    _ => {
                        if self.buf[len - 1] == delim {
                            self.buf.truncate(len - 1);
                        }
                        break;
                    }
                }
            }

            let elem = unsafe { str::from_utf8_unchecked(&self.buf) };
            elem.parse().unwrap_or_else(|_| panic!(format!("failed parsing: {}", elem)))
         }
    }
}



fn main(){
    let stdin = stdin();
    let mut r = utils::StdinReader::new(stdin.lock());
    let n:usize = r.readl();
    let mut l:Vec<usize> = r.read_vec();
    l.sort();
    let mut ans = 0;
    for a_i in 0..(n-2) {
        for b_i in (a_i+1)..(n-1){
            for c_i in (b_i+1)..n{
                let a = l.get(a_i).unwrap();
                let b = l.get(b_i).unwrap();
                let c = l.get(c_i).unwrap();

                if c < &(a + b){
                    ans += 1;
                }
            }
        }
    }
    println!("{}",ans);
}