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.

3

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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.