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 {
  ($($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)*) => {
    #[allow(unused_mut)]
    let mut $var = read_value!($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, [ $t:tt ]) => {{
    let len = read_value!($next, usize);
    (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
  }};

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

fn main() {
  let stack_size = 104_857_600;
  let thd = std::thread::Builder::new().stack_size(stack_size);
  thd.spawn(|| work()).unwrap().join().unwrap();
}

fn work() {
  input! {
    n: usize,
    a: [u32; n],
  }
  a.sort();
  let mut ans = 0;
  for i in 2..n {
    let mut j = i - 1;
    let mut k = 0;
    loop {
      while k < j && a[k] + a[j] <= a[i] {
        k += 1;
      }
      if k == j {
        break;
      }
      ans += j - k;
      j -= 1;
    }
  }
  println!("{}", ans);
}