Maximizing Distinct Frames on a Faulty TV Screen

You are given an old, defective black-and-white TV with a resolution of 100×100 pixels. Each pixel can be either on or off. However, the TV is flawed: its images do not last very long.

A 2×2 pixel block is defined as erroneous if and only if exactly the pixels on one of its diagonals are on. In other words, for a block $$\begin{pmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix} $$

it is erroneous if either

$$a_{11}=1,\;a_{12}=0,\;a_{21}=0,\;a_{22}=1$$

or

$$a_{11}=0,\;a_{12}=1,\;a_{21}=1,\;a_{22}=0.$$

Every second, the TV will flip the state (on becomes off, off becomes on) of at least one pixel that belongs to some erroneous block. For instance, in a 4×4 TV screen example given in the statement, the states evolve over time and eventually cycle (the screen at second 3 equals that at second 1), resulting in 3 distinct frames.

Your task is to construct an initial pixel configuration (a 100×100 grid) that maximizes the number of distinct frames produced by the TV's evolution. This is a submission-answer style problem – you simply output your chosen configuration.

## inputFormat

This problem has no input.

## outputFormat

Output 100 lines, where each line is a string of 100 characters. Each character represents a pixel: '1' for on and '0' for off. The configuration you output will be used as the initial state of the TV screen.

## sample

No input

1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010
0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
... (continues for a total of 100 lines)

$$