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 search(li: &[i32], t: i32) -> usize {
    let mut left = 0;
    let mut right = li.len();
    while right - left > 1 {
        let mid = (right + left) / 2;
        if li[mid] < t {
            right = mid
        } else {
            left = mid
        }
    }
    left
}

fn main() {
    let n: u32 = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned().parse().unwrap()
    };

    let l: Vec<i32> = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let mut ws = s.trim_right().split_whitespace();
        let mut l:Vec<i32> = vec![];
        while let Some(n) = ws.next() {
            l.push(n.parse().unwrap())
        }
        l.sort();
        l.reverse();
        l
    };

    let mut res = 0;
    for i in 0..(n as usize) {
        for j in (i+1)..((n-1) as usize) {
            let t = l[i] - l[j] + 1;
            if t > l[j+1] { continue }
            let cnt = search(&l[j+1..], t);
            res += (cnt+1)
        }
    }
    println!("{}", res)
}