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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let n = read_as_vec::<usize>()[0];

    let ell = read_as_vec::<usize>();

    let mut ab: Vec<(usize, usize)> = Vec::new();

    for i in 0..n{
        for j in i+1..n{
            ab.push((ell[i],ell[j]));
        }
    }

    let mut acc_c = vec![0;2002];

    //count up by the length
    for i in 0..n{
        acc_c[ell[i]] += 1;
    }
    //accumulate
    for i in 1..acc_c.len(){
        acc_c[i] += acc_c[i-1];
    }

    //println!("ll = {:?}", ell);
    let mut ans: usize = 0;
    for (a, b) in ab{
        //println!("-----");
        //println!("{}, {}", a, b);
        let mut diff;
        if a > b{
            diff = a - b;
        }else{
            diff = b - a;
        }
        let sum = a + b;
        //println!("diff = {}, sum = {}", diff, sum);
        let mut maybe_c = acc_c[sum-1] - acc_c[diff];
        //println!("maybec = {}", maybe_c);
        if diff < a && a < sum{
            maybe_c -= 1;
        }

        if diff < b && b < sum{
            maybe_c -= 1;
        }
        //println!("maybec = {}", maybe_c);
        ans += maybe_c;

    }

    println!("{}", ans/3);
}