The border (verge, brink) br of the string S is any proper prefix of this string that is equal to the suffix of S.

A string S = abaababaabaab has two borders (not empty) - ab and abaab. A string S = abaabaab also has two borders - ab and abaab, but the second one is overlapping. A string of length n, formed with a repeating character, like aaaaaaaa (or a8), has n - 1 borders. For the string S = a8 the borders are: a, aa, aaa, aaaa, aaaaa, aaaaaa, aaaaaaa.

The concept of "_proper prefix_" eliminates the border equals to the string.

The length of the border is the number of characters in it.

The common generalization of the concept "border" is the concept of "_biggest border_" - the largest (by number of characters) own prefix equal to its suffix.

Input

Given a string S (|S| ≤ 106).

Output

Print the length of the longest border.