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)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn is_ok(a: u32, b: u32, c: u32) -> bool {
    a < (b + c) && b < (c + a) && c < (a + b)
}

fn solve2(sticks: &[u32], a: u32, b: u32) -> u32 {
    let mut ans: u32 = 0;
    
    for i in 0..sticks.len() {
        if is_ok(a, b, sticks[i]) {
            ans += 1;
        }
    }

    ans
}

fn solve1(sticks: &[u32], a: u32) -> u32 {
    let mut ans: u32 = 0;
    
    for i in 0..sticks.len() - 1 {
        ans += solve2(&sticks[i + 1..], a, sticks[i]);
    }

    ans
}

fn solve(sticks: &Vec<u32>) -> u32 {
    let mut ans: u32 = 0;
    
    for i in 0..sticks.len() - 2 {
        ans += solve1(&sticks[i + 1..], sticks[i]);
    }

    ans
}

fn main(){
    let n: i32 = read();
    let mut sticks: Vec<u32> = (0..n).map(|_| read()).collect();
    sticks.sort();

    println!("{}", solve(&sticks));

    
}