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 (GCC 5.4.1) (judge verdict: Accepted)

char buf[5],out[2<<17];
sz,outsz;
i,j;
N;
char fs[1001]="01213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121412131215121312141213121812131214121312151213121412131216121312141213121512131214121312171213121412131215121312141213121612131214121312151213121412131219121312141213121512131214121312161213121412131215121312141213121712131214121312151213121412131216121312141213121512131214121312181213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121412131215121312141213121:1213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121412131215121312141213121812131214121312151213121412131216121312141213121512131214121312171213121412131215121312141213121612131214121312151213121412131219121312141213121512131214121312161213121412131215121312141213121712131214121312151213121412131216121312141213121512131214121312181213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121";
main(){
	read(0,buf,5);
	for(;;)
	{
		char k=buf[sz++];
		if(k<'0')break;
		N=N*10+k-'0';
	}
	for(;i++<N;)for(j=i;j++<N;)
	{
		out[outsz++]=fs[i^j];
		out[outsz++]='\n';
	}
	write(1,out,outsz);
}