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::stdin;

fn main() {
    let mut first_line = String::new();
    stdin().read_line(&mut first_line).unwrap();
    let n: usize = first_line.trim().parse().unwrap();
    let mut second_line = String::new();
    stdin().read_line(&mut second_line).unwrap();
    let vec: Vec<&str> = second_line.split_whitespace().collect();

    let mut count: u64 = 0;
    for i in 0..n {
        for j in (i + 1)..n {
            for k in (j + 1)..n {
                let a: u32 = vec[i].parse().unwrap();
                let b: u32 = vec[j].parse().unwrap();
                let c: u32 = vec[k].parse().unwrap();
                if a < (b + c) && b < (c + a) && c < (a + b) {
                    count += 1;
                }
            }
        }
    }
    print!("{}", count)
}