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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i

(N - 1).times do |b|
  i = N - b - 1

  a = []
  high_max_loop = 2
  max_loop = 2
  now_loop = 0
  i.times do |j|
    if j % 2 == 0
      a.push(1)
    else
      now_loop += 1
      a.push(now_loop + 1)
      if max_loop == now_loop
        max_loop += 1
        now_loop = 0

        if max_loop == high_max_loop
          high_max_loop += 1
          max_loop = 2
        end
      end
    end
  end
  puts a.join(' ')
end