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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws Exception {
        Main main = new Main();
        main.solve();
    }
    public void solve() throws Exception {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int max_color = 0;
        int current = 1;
        while (current < N) {
            current *= 2;
            max_color += 1;
        }
        int[] nodes = new int[N];
        for (int i = 0; i < N; i++) {
            nodes[i] = i;
        }
        for (int i = 0; i < N-1; i++) {
            int x = nodes[i];
            StringBuilder sb = new StringBuilder();
            for (int j = i + 1; j < N; j++) {
                int y = nodes[j];
                sb.append(level(x, y));
                sb.append(" ");
            }
            System.out.println(sb.substring(0, sb.length()-1));
        }
    }
    private int level(int x, int y) {
        int z = x ^ y;
        int level = 1;
        while ((z & 1) == 0) {
            z = z >> 1;
            level += 1;
        }
        return level;
    }
}