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 n = read::<usize>();
    let mut l = read_vec::<usize>();
    l.sort();

    let mut ret = 0;
    for i in 0..n-1 {
        for j in i+1..n {
            let c = lower_bound(&l, l[i] + l[j]);
            if c > j + 1 {
                ret += c - j - 1;
            }
        }
    }

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

fn lower_bound(v: &Vec<usize>, k: usize) -> usize {
    let mut low = 0;
    let mut high = v.len();

    while low < high {
        let mid = (low + high) / 2;
        if v[mid] < k {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    low
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}