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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int a[999][999],Time=0;
void Deal(vector<int> &tmp)
{
	if(tmp.size()==1)return;
	int lim=tmp.size()/2;
	vector<int> t0,t1;
	for(int p:tmp){
		if(lim)--lim,t0.push_back(p);
		else t1.push_back(p);
	}
	++Time;
	for(int x:t0)
		for(int y:t1)
			a[x][y]=Time;
	Deal(t0),Deal(t1);
}
vector<int> ini;
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)ini.push_back(i);
	Deal(ini);
	for(int i=1;i<n;i++,puts(""))
		for(int j=i+1;j<=n;j++){
			printf("%d",a[i][j]);
			if(j!=n)printf(" ");
		}
	return 0;
}