Problem:
Score: 600 points

Problem Statement

AtCoder's head office consists of N rooms numbered 1 to N. For any two rooms, there is a direct passage connecting these rooms.

For security reasons, Takahashi the president asked you to set a level for every passage, which is a positive integer and must satisfy the following condition:

For each room i\ (1 \leq i \leq N), if we leave Room i, pass through some passages whose levels are all equal and get back to Room i, the number of times we pass through a passage is always even.

Your task is to set levels to the passages so that the highest level of a passage is minimized.

Constraints

N is an integer between 2 and 500 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print one way to set levels to the passages so that the objective is achieved, as follows:

a_{1,2} a_{1,3} ... a_{1,N}
a_{2,3} ... a_{2,N}
.
.
.
a_{N-1,N}

Here a_{i,j} is the level of the passage connecting Room i and Room j.

If there are multiple solutions, any of them will be accepted.

Sample Input 1

3

Sample Output 1

1 2
1

The following image describes this output:

For example, if we leave Room 2, traverse the path 2 \to 3 \to 2 \to 3 \to 2 \to 1 \to 2 while only passing passages of level 1 and get back to Room 2, we pass through a passage six times.

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

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

//{{{ macros missing in 1.15.1
#[macro_use]
mod macros {
    macro_rules! eprint {
        ($($t:tt)*) => {{
            use ::std::io::Write;
            let _ = write!(::std::io::stderr(), $($t)*);
        }};
    }
    macro_rules! eprintln {
        () => { eprintln!(""); };
        ($($t:tt)*) => {{
            use ::std::io::Write;
            let _ = writeln!(::std::io::stderr(), $($t)*);
        }};
    }
    macro_rules! dbg {
        ($val:expr) => {
            match $val {
                tmp => {
                    eprintln!(
                        "[{}:{}] {} = {:#?}",
                        file!(),
                        line!(),
                        stringify!($val),
                        &tmp
                    );
                    tmp
                }
            }
        };
    }
}
//}}}

fn run() {
    let stdin = std::io::stdin();
    let mut sc = Scanner::new(stdin.lock());
    let n: usize = sc.read();
    let mut answer = vec![vec![0; n]; n];
    let mut sets = Vec::new();
    let mut initial = (0..n).collect::<Vec<_>>();
    sets.push(initial);
    let mut level = 1;
    loop {
        let mut next_sets = Vec::new();
        if sets.iter().all(|s| s.len() <= 1) {
            break;
        }
        let mut left = Vec::new();
        let mut right = Vec::new();
        for set in sets {
            let len = set.len();
            let mut new_set1 = Vec::new();
            let mut new_set2 = Vec::new();
            for (i, x) in set.into_iter().enumerate() {
                if i % 2 == 0 {
                    new_set1.push(x);
                    left.push(x);
                } else {
                    new_set2.push(x);
                    right.push(x);
                }
            }
            next_sets.push(new_set1);
            next_sets.push(new_set2);
        }

        for &l in &left {
            for &r in &right {
                if answer[l][r] == 0 {
                    answer[l][r] = level;
                    answer[r][l] = level;
                }
            }
        }

        level += 1;
        sets = next_sets;
    }
    for i in 0..n {
        for j in i + 1..n {
            print!("{}", answer[i][j]);
            if j != n - 1 {
                print!(" ");
            }
        }
        println!("");
    }
}

fn main() {
    std::thread::Builder::new()
        .name("run".to_string())
        .stack_size(1024 * 1024 * 1024)
        .spawn(run)
        .unwrap()
        .join()
        .unwrap()
}

//{{{ Scanner
pub struct Scanner<R> {
    reader: R,
}

impl<R> Scanner<R> {
    pub fn new(r: R) -> Scanner<R> {
        Scanner { reader: r }
    }
}

fn is_whitespace(b: u8) -> bool {
    b == b' ' || b == b'\n' || b == b'\r' || b == b'\t'
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        let buf = std::io::Read::bytes(self.reader.by_ref())
            .map(|b| b.expect("Read failed"))
            .skip_while(|&b| is_whitespace(b))
            .take_while(|&b| !is_whitespace(b))
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error")
    }

    pub fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }

    pub fn read_chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
//}}}