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;
typedef long long ll;
inline int read()
{
	int out=0,fh=1;
	char jp=getchar();
	while ((jp>'9'||jp<'0')&&jp!='-')
		jp=getchar();
	if (jp=='-')
		fh=-1,jp=getchar();
	while (jp>='0'&&jp<='9')
		out=out*10+jp-'0',jp=getchar();
	return out*fh;
}
const int MAXN=1e3+10;
int a[MAXN][MAXN],n;
int fa[MAXN][MAXN];
int Find(int k,int x)
{
	if(fa[k][x]==x)
		return x;
	return fa[k][x]=Find(k,fa[k][x]);
}
void cons()
{
	for(int i=1;i<=1000;++i)
		for(int j=1;j<=n;++j)
			fa[i][j]=j;
	for(int i=1;i<=n;++i)
		for(int j=i+1;j<=n;++j)
		{
			for(int k=1;k<=1000;++k)
				if(Find(k,i)!=Find(k,j))
				{
					int x=Find(k,i),y=Find(k,j);
					fa[k][x]=y;
					a[i][j]=a[j][i]=k;
					break;
				}
		}
}
int main()
{
	n=read();
	cons();
	for(int i=1;i<=n;++i,puts(""))
		for(int j=i+1;j<=n;++j)
			printf("%d ",a[i][j]);
	return 0;
}