Problem B
Association for Cool Machineries (Part 2)

In order to understand this problem, you need to read the “Association for Cool Machineries (Part 1)” problem.

You are the boss of ACM (Association for Cool Machineries), an upstanding company with a single goal of world domination.

Today, after being convinced by the scientific committee of ACM, you learned that GL-bot (shorthand for Giant Laser Robot) is apparently not sapient. Although you still find it difficult to believe that GL-bot is not sapient, yet the scientific committee’s argument is flawless: the movement of GL-bot is too regular for it to originate from free will. However, maybe, if GL-bot is programmed using a particular string and placed on a particular grid, the pattern may be too hard for the scientific committee to notice! This way, it is much harder for them to prove that GL-bot is not sapient, and thus, GL-bot might be labeled as sapient by the scientific committee! Find one such configuration.


This problem has no input (the input will be empty).


Write a valid input for the “Association for Cool Machineries (Part 1)” problem such that when a correct solution to that problem is given your input as its input, its answer is at least $10^6$.

The input must adhere to all the input constraints and restrictions given in the “Association for Cool Machineries (Part 1)” problem. In particular this means that $N$ must be between $3$ and $200$, inclusively.

Sample Data

This problem does not have any sample input and output. See the “Association for Cool Machineries (Part 1)” problem instead for several examples (that is, those sample inputs are in the correct format, but all of them are incorrect for this problem since the answers are less than $10^6$).

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