Problem:
Partition

Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:

Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4 do if A[j] <= x
5 then i = i+1
6 exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1

Note that, in this algorithm, Partition always selects an element A[r] as a pivot element around which to partition the array A[p..r].

Input

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, Ai (i = 1,2,...,n), elements of the sequence are given separated by space characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [  ].

Constraints

1 ≤ n ≤ 100,000

0 ≤ Ai ≤ 100,000

Sample Input 1

12
13 19 9 5 12 8 7 4 21 2 6 11

Sample Output 1

9 5 8 7 4 2 6 [11] 21 13 19 12

Solution in Rust (judge verdict: Accepted)

use std::collections::VecDeque;
use std::env;
//use std::fmt::Debug;
use std::io;
use std::io::prelude::*;
//use std::time::{Duration, Instant};

//===================================================
// MACROs need to be defined above the use place ... ?
macro_rules! dprintln {
    ($($x:expr),*) => {{
        if $crate::is_debug_mode() {
            let f = || {println!( $($x),*)};
            f()
        }
    }}
}

/// Backward For-Loop Helper
///  from -> to (exclude `to`)
///
/// # Examples
/// see tests::macro_backward()
///
#[macro_export]
macro_rules! backward_ho {
    ($from:expr, $to:expr) => {{
        (($to + 1)..($from + 1)).rev()
    }};
}
//===================================================

fn main() {
    // Initialize
    set_debug_mode(false);
    for arg in env::args() {
        if arg == "--debug" {
            set_debug_mode(true);
        }
    }
    dprintln!("[DebugMode] {}", "On");

    // Execute
    dprintln!("=================");
    dprintln!("= READ INPUT     ");
    let stdin = io::stdin();
    let input = BufReadInput::new(stdin.lock());
    dprintln!("[Input] \n{:?}", input);
    dprintln!("=================");
    dprintln!("= INTERPRET INPUT");
    let q = input.into_quiz();
    dprintln!("[Quiz] \n{:?}", q);
    dprintln!("=================");
    dprintln!("= SOLVE QUIZE    ");
    let a = q.solve();
    dprintln!("[Answer] \n{:?}", a);
    dprintln!("=================");
    dprintln!("= PRINT ANSWER   ");
    a.print();
    dprintln!("=================");
}

#[derive(Debug)]
struct Quiz {
    n: usize,    // 1 <= N <= 100,000
    v: Vec<u32>, // 0 <= v[i] <= 100,000, length=N
}

#[derive(Debug)]
struct Answer {
    v: Vec<u32>,
    separator: usize,
}

trait IntoQuiz {
    fn into_quiz(self) -> Quiz;
}

impl<I: Input> IntoQuiz for I {
    fn into_quiz(mut self) -> Quiz {
        let n: usize = self.parse_next().unwrap();
        let v: Vec<u32> = self.parse_next_vec(n).unwrap();
        Quiz { n, v }
    }
}

mod solver{
    pub fn partition(a: &mut[u32], p: usize, r: usize) -> usize {
        dprintln!("partition {:?}", &a[p..r]);
        let x = a[r];
        let mut i = p;
        for j in p..r {
            if a[j] <= x {
                dprintln!(" swap a[{}]:{} <-> a[{}]:{}", i, a[i], j, a[j]);
                a.swap(i, j);
                i += 1;
            }
        }
        dprintln!(" swap a[{}]:{} <-> a[{}]:{}", i, a[i], r, a[r]);
        a.swap(i, r);
        i
    }
}

impl Quiz {
    fn solve(mut self) -> Answer {
        use solver::*;
        let separator = partition(&mut self.v[..], 0usize, self.n-1usize);

        Answer{ 
            v: self.v, 
            separator: separator 
        }
    }
}

impl Answer {
    fn print(self) {
        let iter = self.v.iter().enumerate().map(
            |(idx, num)| if idx == self.separator { 
                format!("[{}]", num)
            } else {
                num.to_string()
            });

        let v: Vec<_> = iter.collect();
        println!("{}", concat_to_string(&v[..]));
    }
}

// =====================================================
// =
// =====================================================

//==================================================
// Stdin Reader
#[derive(Debug)]
pub enum Token {
    Word(String),
    LineBreak,
}

impl Token {
    pub fn is_word(&self) -> bool {
        match *self {
            Token::Word(ref _x) => true,
            _ => false,
        }
    }
}

#[derive(Debug)]
pub struct BufReadInput<R: BufRead> {
    input: R,
    tokens: VecDeque<Token>,
}

pub trait Input {
    fn read_next_word(&mut self) -> Option<Token>;

    fn parse_next<T>(&mut self) -> Option<T>
    where
        T: std::str::FromStr,
    {
        if let Some(Token::Word(str)) = self.read_next_word() {
            match str.parse() {
                Ok(x) => Some(x),
                _ => None,
            }
        } else {
            None
        }
    }

    fn parse_next_vec<T>(&mut self, size: usize) -> Option<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size {
            if let Some(t) = self.parse_next() {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_next_vec2<T>(&mut self, size2: usize, size1: usize) -> Option<Vec<Vec<T>>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size2 {
            if let Some(t) = self.parse_next_vec(size1) {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_all_remaining_into_vec<T>(&mut self) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        loop {
            match self.parse_next() {
                Some(x) => v.push(x),
                None => return v,
            }
        }
    }
}
impl<R: BufRead> BufReadInput<R> {
    pub fn new(input: R) -> Self {
        let tokens = VecDeque::new();

        BufReadInput { input, tokens }
    }
}

impl<R: BufRead> Input for BufReadInput<R> {
    fn read_next_word(&mut self) -> Option<Token> {
        loop {
            match self.tokens.pop_front() {
                None => {
                    // Read Input
                    let mut line = String::new();
                    let n = self.input.read_line(&mut line).expect("Read Error.");
                    if n == 0 {
                        return None;
                    }
                    let mut line_tokens = tokenaize(line);
                    self.tokens.append(&mut line_tokens);
                }
                Some(Token::LineBreak) => (),
                x => return x,
            }
        }
    }

}

//TODO: Make CaseIterator
// ex) 
//  let mut input: Input ...
//  let mut iter: CaseIterator<Case=Command> = input.rest_into_cases(|i|   
//    let cmd:String = i.parse_next().expect("Parse error cmd");
//    let num:u32    = i.parse_next().expect("Parse error num");
//
//    Command::new(cmd, num)
//  );
//  let case1 = iter.next();
//  let case2 = iter.next();
//  ...


fn tokenaize(str: String) -> VecDeque<Token> {
    let mut v = VecDeque::new();

    for w in str.split_whitespace() {
        v.push_back(Token::Word(w.to_string()));
    }
    v.push_back(Token::LineBreak);
    v
}

//==================================================
// Utility Functions
pub fn concat_vec_to_string<T>(v: &Vec<T>) -> String
where
    T: std::fmt::Display,
{
    let mut string = String::with_capacity(v.len() * 2);

    if let Some((h, t)) = v.split_first() {
        string = h.to_string();

        for obj in t {
            string.push(' ');
            string.push_str(&obj.to_string());
        }
    }

    return string;
}

//
pub fn concat_to_string<T>(v: &[T]) -> String
where
    T: std::fmt::Display,
{
    let mut ret = String::with_capacity(v.len() * 2);

    if let Some((h, t)) = v.split_first() {
        ret = h.to_string();

        for obj in t {
            ret.push(' ');
            ret.push_str(&obj.to_string());
        }
    }

    ret
}

//==================================================
// Debug Switch
static mut S_DEBUG_MODE: bool = false;
fn is_debug_mode() -> bool {
    unsafe { S_DEBUG_MODE }
}

fn set_debug_mode(mode: bool) {
    unsafe {
        S_DEBUG_MODE = mode;
    }
}

//==================================================
// Usage
#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn macro_backward() {
        let mut v = Vec::new();
        for i in backward_ho!(5, 1) {
            v.push(i);
        }
        assert_eq!(vec![5, 4, 3, 2], v);
    }
}