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<bits/stdc++.h>
using namespace std;
int f(int x,int y,int n){
if(x<=n/2 && n/2+1<=y)
  return 1;
  else if(x<=n/2 &&y<=n/2)
    return f(x,y,n/2)+1;
  else
    return f(x-n/2,y-n/2,n-n/2)+1;
}
int main(){
  int N;cin>>N;
  for(int i=1;i<N;i++){
  for(int j=i+1;j<N;j++)
    cout<<f(i,j,N)<<" ";
    cout<<f(i,N,N)<<endl;
   }
  return 0;
}