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: Wrong Answer)

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 l: Vec<usize> = l.split_whitespace().map(|s| s.parse().unwrap()).collect();

    let mut count: Vec<usize> = vec![0; 1002];
    for &length in l.iter() {
        count[length + 1] += 1;
    }
    for i in 1..1002 {
        count[i] += count[i - 1];
    }

    let mut ans = 0;
    for i in 0..n {
        for j in i + 1..n {
            let a = std::cmp::min(l[i], l[j]);
            let b = std::cmp::max(l[i], l[j]);
            let sum = std::cmp::min(a + b, 1001);
            ans += count[sum] - count[b] - 1;
            if a == b {
                ans -= 1;
            }
        }
    }

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