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::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let m = 1000;
    let mut cnt = vec![0u64; 2 * m + 1];
    for _ in 0..n {
        let l: usize = it.next().unwrap().parse().unwrap();
        cnt[l] += 1;
    }
    for i in 1..(2 * m + 1) {
        cnt[i] += cnt[i - 1];
    }
    let mut ans = 0u64;
    for a in 1..(m + 1) {
        for b in a..(m + 1) {
            if a == b {
                let x = cnt[a] - cnt[a - 1];
                ans += x * (x - 1) * (x - 2) / 6;
                ans += x * (x - 1) / 2 * (cnt[a + b - 1] - cnt[a]);
            } else {
                let x = cnt[a] - cnt[a - 1];
                let y = cnt[b] - cnt[b - 1];
                ans += x * y * (y - 1) / 2;
                ans += x * y * (cnt[a + b - 1] - cnt[b]);
            }
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}