On the skin of a Rhinoceros, its folds are vertical and horizontal. If the Rhinoceros has \(a\) vertical and \(b\) horizontal folds on the left side, and on the right side – \(c\) vertical and \(d\) horizontal folds, we will say that this is a rhinoceros in the state \((abcd)\) or just an \((abcd)\) rhinoceros.
If the Rhinoceros’ itches one of his sides against a tree in an up-down movement, and Rhinoceros has two horizontal folds on this side, then these two horizontal folds are smoothed out. If there are no two folds like this, then nothing happens.
Similarly, if the Rhinoceros itches on of his sides in a back and forth movement, and on this side, there are two vertical folds, then they are smoothed out. If there are no two folds like this, then nothing happens.
If, on some side, two folds are smoothed out, then on the other side, two new folds immediately appear: one vertical and one horizontal.
The rhinoceroses often have random sides that are itchy and need to be scratched against a tree in random directions.
At first there was a herd of Rhinoceroses in the savannah \((0221)\). Prove that after some time there were Rhinoceros of state \((2021)\) in the savannah.