Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length n, a_1, ..., a_n.
Let us consider performing the following n operations on an empty sequence b.

The i-th operation is as follows:

Append a_i to the end of b.

Reverse the order of the elements in b.

Find the sequence b obtained after these n operations.

Constraints

1 \leq n \leq 2\times 10^5

0 \leq a_i \leq 10^9

n and a_i are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print n integers in a line with spaces in between.
The i-th integer should be b_i.

Sample Input 1

4
1 2 3 4

Sample Output 1

4 2 1 3

After step 1 of the first operation, b becomes: 1.

After step 2 of the first operation, b becomes: 1.

After step 1 of the second operation, b becomes: 1, 2.

After step 2 of the second operation, b becomes: 2, 1.

After step 1 of the third operation, b becomes: 2, 1, 3.

After step 2 of the third operation, b becomes: 3, 1, 2.

After step 1 of the fourth operation, b becomes: 3, 1, 2, 4.

After step 2 of the fourth operation, b becomes: 4, 2, 1, 3.

Thus, the answer is 4 2 1 3.

Sample Input 2

3
1 2 3

Sample Output 2

3 1 2

As shown above in Sample Output 1, b becomes 3, 1, 2 after step 2 of the third operation. Thus, the answer is 3 1 2.

Sample Input 3

1
1000000000

Sample Output 3

1000000000

Sample Input 4

6
0 6 7 6 7 0

Sample Output 4

0 6 6 0 7 7

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

use std::io::*;
use std::str::FromStr;
use std::collections::HashMap;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn print_s(s: &Vec<char>) {
    for &c in s.iter() {
        print!("{}", c);
    }
    println!("");
}

fn expand_s(s: &Vec<char>) -> Vec<char> {
    let mut skip = 0;
    'inner_loop: for i in s.len() / 2 + 1..s.len() {
        for j in i..s.len() {
            if s[j] != s[j - i] {
                continue 'inner_loop;
            }
        }
        skip = s.len() - i;
        break;
    }
    // println!("{}", skip);
    let ret = s.iter()
        .chain(s[skip..s.len() - skip].iter())
        .cloned()
        .collect::<Vec<_>>();

    // check
    assert!(ret.len() % 2 == 0);
    for i in 0..ret.len() / 2 {
        assert!(ret[i] == ret[i + ret.len() / 2]);
    }
    ret
}

#[allow(dead_code)]
fn naive(s: &Vec<char>, l: usize, r: usize) -> Vec<usize> {
    let mut s = s.clone();
    while s.len() < r {
        s = expand_s(&s);
    }
    let mut cnts = vec![0; 26];
    for i in l..r {
        cnts[(s[i] as u8 - 'a' as u8) as usize] += 1;
    }
    cnts
}

fn solve(s: &Vec<char>, l: usize, r: usize) -> Vec<usize> {
    let mut temp_s = s.clone();
    let mut lens = vec![s.len()];
    for _ in 0..2 {
        temp_s = expand_s(&temp_s);
        lens.push(temp_s.len());
    }
    // println!("{:?}", lens);
    for i in 2.. {
        if r <= lens[i] {
            break;
        }
        if lens[0] + lens[1] == lens[2] {
            let v = lens[i - 1] + lens[i];
            lens.push(v);
        } else {
            // assert!(lens[2] - lens[1] == lens[1] - lens[0]);
            let v = lens[i] + (lens[i] - lens[i - 1]);
            lens.push(v);
        }
    }
    // println!("{:?}", lens);
    let mut ranges = HashMap::<(usize, usize), usize>::new();
    ranges.insert((l, r), 1);
    for i in (1..lens.len()).rev() {
        let mut nranges = HashMap::<(usize, usize), usize>::new();
        let skip = lens[i - 1] - lens[i] / 2;
        let prev = lens[i - 1];
        for (&range, &cnt) in ranges.iter() {
            if range.1 <= prev {
                *nranges.entry(range).or_insert(0) += cnt;
            } else if prev <= range.0 {
                let offset = range.0 - prev;
                *nranges
                    .entry((skip + offset, range.1 - prev + skip))
                    .or_insert(0) += cnt;
            } else {
                *nranges.entry((range.0, prev)).or_insert(0) += cnt;
                *nranges.entry((skip, range.1 - prev + skip)).or_insert(0) += cnt;
                assert!(range.1 - prev + skip <= prev);
                assert!(prev - range.0 + range.1 - prev + skip - skip == range.1 - range.0);
            }
        }
        ranges = nranges;
    }
    let mut cnts = vec![0; 26];
    for (&range, &cnt) in ranges.iter() {
        for i in range.0..range.1 {
            cnts[(s[i] as u8 - 'a' as u8) as usize] += cnt;
        }
    }
    cnts
}

fn main() {
    let s = read::<String>().chars().collect::<Vec<char>>();
    let l = read::<usize>() - 1;
    let r = read::<usize>();
    let cnts = solve(&s, l, r);
    for i in 0..26 {
        if i != 0 {
            print!(" ");
        }
        print!("{}", cnts[i]);
    }
    println!("");
}