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.

Example

Input

3


Output

1 2
1
#include<iostream>
using namespace std;

int main(){
  int N;
  cin >> N;

  int highest_bit_N = 0;
  for(; (1 << highest_bit_N) <= N - 1; highest_bit_N++){
  }
  // N = 4 -> 2
  // N = 5 -> 3
  // cout << highest_bit_N << endl;

  for(int i = 0; i < N - 1; i++){
    for(int j = i + 1; j < N; j++){
      if(j != i + 1){
        cout << ' ';
      }
      int highest_diff_bit = 10;
      while((i & (1 << highest_diff_bit)) == (j & (1 << highest_diff_bit))){
        highest_diff_bit--;
      }
      cout << highest_diff_bit + 1;
    }
    cout << endl;
  }
}
