Problem:
Score : 300 points

Problem Statement

There are 3N participants in AtCoder Group Contest.
The strength of the i-th participant is represented by an integer a_i.
They will form N teams, each consisting of three participants.
No participant may belong to multiple teams.

The strength of a team is defined as the second largest strength among its members.
For example, a team of participants of strength 1, 5, 2 has a strength 2, and a team of three participants of strength 3, 2, 3 has a strength 3.

Find the maximum possible sum of the strengths of N teams.

Constraints

1 ≤ N ≤ 10^5

1 ≤ a_i ≤ 10^{9}

a_i are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the answer.

Sample Input 1

2
5 2 8 5 1 5

Sample Output 1

10

The following is one formation of teams that maximizes the sum of the strengths of teams:

Team 1: consists of the first, fourth and fifth participants.

Team 2: consists of the second, third and sixth participants.

Sample Input 2

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 2

10000000000

The sum of the strengths can be quite large.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

use nyan::*;

fn main() {
    let stdin = std::io::stdin();
    let mut sc = Scanner::new(stdin.lock());

    let n: usize = sc.read();
    let mut a: Vec<u64> = sc.read_vec(n * 3);

    a.sort();

    let mut ans = 0;
    for i in 0..n {
        ans += a[n + i * 2];
    }

    println!("{}", ans);
}

#[allow(dead_code)]
mod nyan {
    use std::cmp::Ordering;
    use std::fmt::{Debug, Display};
    use std::io;
    use std::iter::{self, FromIterator};
    use std::str::FromStr;

    // https://doc.rust-lang.org/1.39.0/src/core/num/mod.rs.html#4473-4523
    #[inline]
    pub fn is_ascii_whitespace(c: char) -> bool {
        match c {
            '\t' | '\n' | '\x0C' | '\r' | ' ' => true,
            _ => false,
        }
    }

    #[inline]
    pub fn is_ascii_linebreak(c: char) -> bool {
        match c {
            '\n' | '\r' => true,
            _ => false,
        }
    }

    pub struct Scanner<R: io::BufRead> {
        reader: R,
        buffer: String,
        cursor: usize,
    }

    impl<R: io::BufRead> Scanner<R> {
        pub fn new(reader: R) -> Scanner<R> {
            Scanner {
                reader: reader,
                buffer: String::with_capacity(32),
                cursor: 0,
            }
        }

        fn next<F: Fn(char) -> bool>(&mut self, f: F) -> io::Result<&str> {
            loop {
                if let Some(l) = self.buffer[self.cursor..].find(|c| !is_ascii_whitespace(c)) {
                    self.cursor += l;
                    break;
                }

                self.buffer.clear();
                self.cursor = 0;
                match self.reader.read_line(&mut self.buffer) {
                    Err(e) => return Err(e),
                    Ok(0) => return Err(io::Error::from(io::ErrorKind::UnexpectedEof)),
                    _ => (),
                }
            }

            let start = self.cursor;
            self.cursor = self.buffer[self.cursor..]
                .find(f)
                .map_or(self.buffer.len(), |l| start + l);
            Ok(&self.buffer[start..self.cursor])
        }

        fn next_word(&mut self) -> io::Result<&str> {
            self.next(|c| is_ascii_whitespace(c))
        }

        fn next_line(&mut self) -> io::Result<&str> {
            self.next(|c| c == '\n' || c == '\r')
        }

        pub fn read<T>(&mut self) -> T
        where
            T: FromStr,
            <T as FromStr>::Err: Debug,
        {
            self.next_word().unwrap().parse().unwrap()
        }

        pub fn read_vec<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromStr,
            <U as FromStr>::Err: Debug,
        {
            (0..n).map(|_| self.read()).collect()
        }

        pub fn read_vec2d<T, U, V>(&mut self, m: usize, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<V>,
            V: FromStr,
            <V as FromStr>::Err: Debug,
        {
            (0..m).map(|_| self.read_vec(n)).collect()
        }

        pub fn read_line<T: FromIterator<char>>(&mut self) -> T {
            self.next_line().unwrap().chars().collect()
        }

        pub fn read_lines<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<char>,
        {
            (0..n).map(|_| self.read_line()).collect()
        }
    }

    #[test]
    fn test_scanner_next_word() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert_eq!(r.next_word().unwrap(), "foo");
        assert_eq!(r.next_word().unwrap(), "bar");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    #[test]
    fn test_scanner_next_line() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_line().unwrap(), "hello world");
        assert_eq!(r.next_line().unwrap(), "foo");
        assert_eq!(r.next_line().unwrap(), "bar");
        assert!(r.next_line().is_err());
        assert!(r.next_line().is_err());
    }

    #[test]
    fn test_scanner_no_linebreak() {
        let buf = io::Cursor::new(b"hello world");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    pub fn print_vec<T: Display>(v: &[T]) {
        if v.is_empty() {
            return;
        }

        print!("{}", v[0]);
        for i in v.iter().skip(1) {
            print!(" {}", i);
        }
        println!();
    }

    // C++ like binary search functions (upper_bound, lower_bound, equal_range)
    pub trait BinarySearch<T> {
        fn lower_bound(&self, value: &T) -> usize;
        fn upper_bound(&self, value: &T) -> usize;
        fn equal_range(&self, value: &T) -> (usize, usize) {
            (self.lower_bound(value), self.upper_bound(value))
        }
    }

    impl<T: Ord> BinarySearch<T> for [T] {
        // https://en.cppreference.com/w/cpp/algorithm/lower_bound#Possible_implementation
        fn lower_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Less => first = mid + 1,
                    _ => last = mid,
                }
            }
            first
        }

        // https://en.cppreference.com/w/cpp/algorithm/upper_bound#Possible_implementation
        fn upper_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Greater => last = mid,
                    _ => first = mid + 1,
                }
            }
            first
        }
    }

    #[test]
    pub fn test_binary_search() {
        let data = vec![1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6];
        assert_eq!(data.lower_bound(&4), 7);
        assert_eq!(data.upper_bound(&4), 10);
    }

    // https://doc.rust-lang.org/std/cmp/struct.Reverse.html
    #[derive(PartialEq, Eq, Debug)]
    pub struct Rev<T>(pub T);

    impl<T: PartialOrd> PartialOrd for Rev<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }

    impl<T: Ord> Ord for Rev<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    // Extended Euclidean algorithm
    // ax + by = gcd(x, y)
    pub fn extended_gcd(a: u64, b: u64) -> (u64, i64, i64) {
        if b == 0 {
            (a, 1, 0)
        } else {
            let (m, y, x) = extended_gcd(b, a % b);
            (m, x, y - (a / b) as i64 * x)
        }
    }

    pub fn gcd(a: u64, b: u64) -> u64 {
        if b == 0 {
            a
        } else {
            gcd(b, a % b)
        }
    }

    pub fn lcm(a: u64, b: u64) -> u64 {
        a / gcd(a, b) * b
    }

    // x^n (mod p)
    pub fn pow_mod(mut x: u64, mut n: u64, p: u64) -> u64 {
        let mut r = 1;
        while n > 0 {
            if n & 1 > 0 {
                r *= x;
                r %= p;
            }
            x *= x;
            x %= p;
            n >>= 1;
        }
        r
    }

    #[test]
    fn test_pow_mod() {
        assert_eq!(pow_mod(4, 13, 497), 445);
        assert_eq!(pow_mod(2, 90, 13), 12);
        assert_eq!(pow_mod(2, 99999999, 147), 134);
    }

    // a^{p-1} = 1 (mod p) (Fermat's little theorem)
    // a^{p - 2} * a = 1 → a^{-1} = a^{p-2}
    pub fn inv_mod(n: u64, p: u64) -> u64 {
        pow_mod(n, p - 2, p)
    }

    // s * (s + 1) * .. * t (mod p)
    pub fn prod_mod(s: u64, t: u64, p: u64) -> u64 {
        (s..t + 1).fold(1, |acc, x| acc * x % p)
    }

    // nCk (mod p)
    pub fn comb_mod(n: u64, k: u64, p: u64) -> u64 {
        // nCk = n! / (k! * (n - k)!)
        //     = ((n-k+1) * (n-k+2) * ... * n) * inv(k!)
        prod_mod(n - k + 1, n, p) * inv_mod(prod_mod(1, k, p), p) % p
    }

    // comb_mod_multi(n_max, p)(n, k) = nCk (mod p)
    pub fn comb_mod_multi(n_max: u64, p: u64) -> Box<Fn(u64, u64) -> u64> {
        // fact[n] = n!, fact_inv[n] = (n!)^(-1) (mod p)
        let fact = iter::once(1)
            .chain(1..n_max + 1)
            .scan(1, |state, x| {
                *state = (*state * x) % p;
                Some(*state)
            })
            .collect::<Vec<_>>();
        let fact_inv = fact.iter().map(|&x| inv_mod(x, p)).collect::<Vec<_>>();

        Box::new(move |n, k| {
            let a = fact[n as usize];
            let b = fact_inv[k as usize];
            let c = fact_inv[(n - k) as usize];
            (((a * b) % p) * c) % p
        })
    }

    #[inline]
    pub fn minmax<T: Ord>(a: T, b: T) -> (T, T) {
        if a < b {
            (a, b)
        } else {
            (b, a)
        }
    }

    #[test]
    fn test_minmax() {
        assert_eq!(minmax(1, 3), (1, 3));
        assert_eq!(minmax(3, 1), (1, 3));
    }

    #[inline]
    pub fn digits(x: u64, base: u64) -> u32 {
        (1..)
            .find(|&i| base.pow(i - 1) <= x && x < base.pow(i))
            .unwrap_or(0)
    }

    #[test]
    fn test_digits() {
        assert_eq!(digits(1234, 10), 4);
        assert_eq!(digits(1234567890, 10), 10);
        assert_eq!(digits(0xdeadbeef, 16), 8);
        assert_eq!(digits(0o123456, 8), 6);
        assert_eq!(digits(0b10101, 2), 5);
    }

    pub struct UnionFind {
        n: usize,
        root: Vec<usize>,
        rank: Vec<usize>,
        size: Vec<usize>,
    }

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            UnionFind {
                n: n,
                root: (0..n).collect(),
                rank: vec![0; n],
                size: vec![1; n],
            }
        }

        pub fn root(&mut self, x: usize) -> usize {
            let r = self.root[x];
            if r == x {
                r
            } else {
                self.root[x] = self.root(r);
                self.root[x]
            }
        }

        pub fn merge(&mut self, x: usize, y: usize) {
            let rx = self.root(x);
            let ry = self.root(y);
            if rx == ry {
                return;
            }

            if self.rank[rx] < self.rank[ry] {
                self.root[rx] = ry;
                self.size[ry] += self.size[rx];
            } else {
                self.root[ry] = rx;
                self.size[rx] += self.size[ry];
                if self.rank[rx] == self.rank[ry] {
                    self.rank[rx] += 1;
                }
            }
        }

        pub fn size(&mut self, x: usize) -> usize {
            let rx = self.root(x);
            self.size[rx]
        }
    }
}