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: Wrong Answer)

// Rustで競技プログラミングの入力をスッキリ記述するマクロ
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8

use std::fmt;

use std::ops::Index;

#[derive(Debug, Clone)]
pub struct LazyBuffer<I: Iterator> {
    pub it: I,
    done: bool,
    buffer: Vec<I::Item>,
}

impl<I> LazyBuffer<I>
where
    I: Iterator,
{
    pub fn new(it: I) -> LazyBuffer<I> {
        let mut it = it;
        let mut buffer = Vec::new();
        let done;
        if let Some(first) = it.next() {
            buffer.push(first);
            done = false;
        } else {
            done = true;
        }
        LazyBuffer {
            it: it,
            done: done,
            buffer: buffer,
        }
    }

    pub fn len(&self) -> usize {
        self.buffer.len()
    }

    pub fn is_done(&self) -> bool {
        self.done
    }

    pub fn get_next(&mut self) -> bool {
        if self.done {
            return false;
        }
        let next_item = self.it.next();
        match next_item {
            Some(x) => {
                self.buffer.push(x);
                true
            }
            None => {
                self.done = true;
                false
            }
        }
    }
}

impl<I, J> Index<J> for LazyBuffer<I>
where
    I: Iterator,
    I::Item: Sized,
    Vec<I::Item>: Index<J>
{
    type Output = <Vec<I::Item> as Index<J>>::Output;

    fn index(&self, _index: J) -> &Self::Output {
        self.buffer.index(_index)
    }
}

/// An iterator to iterate through all the `k`-length combinations in an iterator.
///
/// See [`.combinations()`](../trait.Itertools.html#method.combinations) for more information.
#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
pub struct Combinations<I: Iterator> {
    k: usize,
    indices: Vec<usize>,
    pool: LazyBuffer<I>,
    first: bool,
}

macro_rules! debug_fmt_fields {
    ($tyname:ident, $($($field:ident).+),*) => {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            f.debug_struct(stringify!($tyname))
                $(
              .field(stringify!($($field).+), &self.$($field).+)
              )*
              .finish()
        }
    }
}

impl<I> fmt::Debug for Combinations<I>
    where I: Iterator + fmt::Debug,
          I::Item: fmt::Debug,
{
    debug_fmt_fields!(Combinations, k, indices, pool, first);
}

/// Create a new `Combinations` from a clonable iterator.
pub fn combinations<I>(iter: I, k: usize) -> Combinations<I>
    where I: Iterator
{
    let mut indices: Vec<usize> = Vec::with_capacity(k);
    for i in 0..k {
        indices.push(i);
    }
    let mut pool: LazyBuffer<I> = LazyBuffer::new(iter);

    for _ in 0..k {
        if !pool.get_next() {
            break;
        }
    }

    Combinations {
        k: k,
        indices: indices,
        pool: pool,
        first: true,
    }
}

impl<I> Iterator for Combinations<I>
    where I: Iterator,
          I::Item: Clone
{
    type Item = Vec<I::Item>;
    fn next(&mut self) -> Option<Self::Item> {
        let mut pool_len = self.pool.len();
        if self.pool.is_done() {
            if pool_len == 0 || self.k > pool_len {
                return None;
            }
        }

        if self.first {
            self.first = false;
        } else if self.k == 0 {
            return None;
        } else {
            // Scan from the end, looking for an index to increment
            let mut i: usize = self.k - 1;

            // Check if we need to consume more from the iterator
            if self.indices[i] == pool_len - 1 && !self.pool.is_done() {
                if self.pool.get_next() {
                    pool_len += 1;
                }
            }

            while self.indices[i] == i + pool_len - self.k {
                if i > 0 {
                    i -= 1;
                } else {
                    // Reached the last combination
                    return None;
                }
            }

            // Increment index, and reset the ones to its right
            self.indices[i] += 1;
            let mut j = i + 1;
            while j < self.k {
                self.indices[j] = self.indices[j - 1] + 1;
                j += 1;
            }
        }

        // Create result vector based on the indices
        let mut result = Vec::with_capacity(self.k);
        for i in self.indices.iter() {
            result.push(self.pool[*i].clone());
        }
        Some(result)
    }
}

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)*}
    };
}

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)*}
    };
}

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")
    };
}

use std::collections::HashSet;

fn main() {
    input! {
        n: usize,
        v: [i32; n]
    };
    let mut v = v;
    let set: HashSet<_> = v.drain(..).collect(); // dedup
    let c = combinations(set.iter(), 3);
    let mut z = 0;
    for i in c {
        let a = *i[0];
        let b = *i[1];
        let c = *i[2];
        if a < b + c && b < c + a && c < a + b  {
            z += 1;
        }
    }
    println!("{}", z);
}