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 (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        mut l: [isize;n],
    }

    let mut ans = 0;
    l.sort();
    for i in 0..l.len() {
        for j in i + 1..l.len() {
            let ret = lower_bound(&l, l[i] + l[j], |x, y| x >= y);
            ans += ret - j as isize - 1;
        }
    }

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

fn lower_bound(v: &Vec<isize>, key: isize, compare: fn(isize, isize) -> bool) -> isize {
    let mut ng = -1;
    let mut ok = v.len() as isize;
    while (ok - ng).abs() > 1 {
        let mid = (ok + ng) / 2;
        if compare(v[mid as usize], key) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    ok
}