Facets of the string

A border of a string $T$ is defined as a proper prefix that is also equal to a suffix (the entire string is not considered a proper prefix). For example, the string T = abaababaabaab has two non-empty borders: ab and abaab. Similarly, the string T = abaabaab also has two non-empty borders: ab and abaab, with the second border overlapping its prefix. A string consisting of identical characters has n-1 borders; for example, T = aaaaaaaa has the borders: a, aa, aaa, aaaa, aaaaa, aaaaaa, aaaaaaa. The length of a border is the number of characters it contains. Among all borders, the largest border is the longest proper prefix that is also a suffix.

Your task is to find the length of the largest border of the given string $T$.