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)

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();

    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut l_s = buf.split_whitespace()
        .map(|x| x.parse::<usize>().unwrap())
        .collect::<Vec<_>>();

    l_s.sort();

    let mut ans = 0usize;

    for a in 0..l_s.len() {
        for b in (a+1)..l_s.len() {
            let c_over = l_s[a] + l_s[b];

            let mut l = b;
            let mut r = l_s.len();
            let mut mid = (l + r) / 2;

            while r - l > 1 {
                if l_s[mid] < c_over {
                    l = mid;
                } else {
                    r = mid;
                }
                mid = (l + r) / 2;
            }

            ans += mid - b;
        }
    }

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