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)

// -*- coding:utf-8-unix -*-

use proconio::input;

// v[i] >= k を満たす最小の i
fn lower_bound(v: &[u32], k: u32) -> 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 main() {
    input! {
        n: usize,
        mut l: [u32; n],
    }

    l.sort();
    let mut ans = 0;
    for i in 0..n {
        for j in i + 1..n {
            // let k = lower_bound(&l, l[i] + l[j]);
            // ans += k - (j + 1);
            let k = lower_bound(&l[j + 1..], l[i] + l[j]);
            ans += k;
        }
    }
    println!("{}", ans);
}