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: Time Limit Exceeded)

#[allow(unused_imports)]
use proconio::{fastout, input};
use std::cmp::Reverse;

#[fastout]
fn main() {
    input!(n: usize, mut l: [usize; n]);
    let mut count = 0;

    let mut ans_vec = vec![vec![0; n]; n];

    l.sort_unstable_by_key(|&x| Reverse(x));
    for i in 0..n {
        for j in 0..n {
            ans_vec[i][j] = l[i] + l[j];
        }
    }

    for i in 0..n {
        for j in i + 1..n {
            for k in j + 1..n {
                if !l[k] < ans_vec[j][i] {
                    break;
                }

                if l[i] < ans_vec[j][k] && l[j] < ans_vec[i][k] {
                    count += 1;
                }
            }
        }
    }

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