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)


#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(dead_code)]
fn lower_bound(v: Vec<i32>, search_num: i32) -> usize {

    0
}

fn main() {
    input!{
        n: usize,
        l: [i32; n],
    }

    println!("{}", syakutori_method(n, l));
    // println!("{}", use_rs_binaly_search(n, l));
}

#[allow(dead_code)]
fn syakutori_method(n: usize, l: Vec<i32>) -> i32 {
    let mut l = l;
    l.sort();
    let l = l;
    let mut answer = 0;

    for fst_i in 0..n {
        let mut lim = fst_i;
        for snd_i in fst_i+1..n {
            while lim < n && l[lim] < l[fst_i] + l[snd_i] { lim+=1; }
            answer += lim - (snd_i + 1);
        }
    }
    answer as i32
}

#[allow(dead_code)]
fn mine_binaly_search(n: usize, l: Vec<i32>) -> i32 {
    let mut l = l;
    l.sort();
    let l = l;
    let mut answer: i32 = 0;
    for i in 0..n {
        for u in i+1..n {
            let k = lower_bound(l.to_vec(), l[i] + l[u]);
            answer += std::cmp::max(0, k - u) as i32;
        }
    }
    answer
}

#[allow(dead_code)]
fn use_rs_binaly_search(n: usize, l: Vec<i32>) -> i32 {
    let mut l = l;
    l.sort();
    let l = l;
    let mut answer: i32 = 0;
    for i in 0..n {
        for u in i+1..n {
            let up_lim = l[i] + l[u];
            let point = match l.binary_search(&(up_lim - 1)) {
                Ok(x) => x,
                Err(y) => y - 1
            };
            answer += std::cmp::max(0, point - u) as i32;
        }
    }
    answer
}