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 (1.42.0) (judge verdict: Wrong Answer)

#![allow(dead_code, unused_imports, deprecated)]
use std::cmp::{max, min, Reverse};
use std::collections::HashMap;
use itertools::Itertools;
use maplit::*;
use proconio::{input, fastout};
use proconio::marker::*;

const INF: usize = 1_000_000_007;

#[fastout] 
fn main() {
  input!{
    n : usize,
    mut l : [isize; n],
  };
  
  l.sort();
  
  let mut res = 0usize;
  for k in 2..n {
    for j in 1..k {
      let (b, c) = (l[j], l[k]);
      let lb = match l[0..j].binary_search(&(c - b + 1)) {
        Ok(i) => i,
        Err(i) => i,
      };
      let ub = match l[0..j].binary_search(&(c + b + 1)) {
        Ok(i) => i,
        Err(i) => i,
      };
      res += ub - lb;
    }
  }

  println!("{}", res);
}