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)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let mut apexes = 1;
    let mut max_level = 0;

    while apexes < n {
        apexes *= 2;
        max_level += 1;
    }
    debug!(max_level);
    let mut levels = vec![vec![false; max_level]; n];

    for i in 0..n {
        for j in 0..max_level {
            if i >> j & 1 == 0 {
                levels[i][j] = true;
            }
        }
    }

    let mut graph = vec![vec![0; n]; n]; // level
    for i1 in 0..n {
        for i2 in i1 + 1..n {
            for j in 0..max_level {
                if levels[i1][j] != levels[i2][j] {
                    graph[i1][i2] = j;
                }
            }
        }
    }
    debug!(graph);
    for i in 0..n - 1 {
        let ans = graph[i][i + 1..n]
            .iter()
            .map(|&x| x + 1)
            .collect::<Vec<_>>();
        print_array(&ans);
    }
}

fn print_array<T: std::string::ToString>(array: &Vec<T>) {
    println!(
        "{}",
        array
            .iter()
            .map(|ref x| x.to_string())
            .collect::<Vec<_>>()
            .join(" ")
    );
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}