quadratic arrangement

In the list of characters in the first line, each character occurs only once. Therefore, the first line is an alphabet. Based on the alphabet, a character is assigned a zero-based index; the second character has index one. The second line is obtained from the first line by shifting the first line to the left by single step, moving the character from the leftmost position of the first line to the rightmost position of the second line. It can be said that the second line results from shifting the first line cyclically to the left by single step. In total, any line is obtained from the first line by shifting the first line cyclically to the left by the number of steps given by the index of the character located at the leftmost position of the line. If a line is cyclically shifted to the left, it can be said that each character is cyclically left-shifted. The minimum positive number of steps that is sufficient to reproduce a character by cyclically left-shifting, is given by the number of characters in the alphabet.

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