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)

// 標準入力から一行を読み取り、指定の型に変換する
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    let number: i32 = read();
    let mut sticks: Vec<i32> = read_vec();

    let mut count_of_triangles: i32 = 0;

    loop
    {
        for b in 1..sticks.len() {
            for c in 2..sticks.len() {
                if b >= c { continue; }
                count_of_triangles += 
                if (sticks[0] < sticks[b] + sticks[c]) &&
                   (sticks[b] < sticks[c] + sticks[0]) &&
                   (sticks[c] < sticks[0] + sticks[b]) { 1 } else { 0 };
            }
        }
        sticks.remove(0);
        if sticks.len() < 3 { break; }
    }

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