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::{self, BufRead};

fn main() {
    let stdin = io::stdin();
    let mut lines = stdin.lock().lines();
    let n: usize = lines.next().unwrap().unwrap().parse().unwrap();
    let l = lines.next().unwrap().unwrap();
    let mut l: Vec<usize> = l.split_whitespace().map(|s| s.parse().unwrap()).collect();
    l.sort();

    let mut ans = 0;
    for i in 0..n {
        for j in i + 1..n {
            let a = l[i];
            let b = l[j];

            let mut left = j;
            let mut right = n;
            while right - left > 1 {
                let middle = (left + right) / 2;
                if l[middle] < a + b {
                    left = middle;
                } else {
                    right = middle;
                }
            }

            ans += left - j;
        }
    }

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