We call a sequence of strings t₁, ..., t_k a journey of length k, if for each i > 1 t_i is a substring of t_i - 1 and length of t_i is strictly less than length of t_i - 1. For example, {ab, b} is a journey, but {ab, c} and {a, a} are not.

Define a journey on string s as journey t₁, ..., t_k, such that all its parts can be nested inside s in such a way that there exists a sequence of strings u₁, ..., u_k + 1 (each of these strings can be empty) and s = u₁ t₁ u₂ t₂... u_k t_k u_k + 1. As an example, {ab, b} is a journey on string abb, but not on bab because the journey strings t_i should appear from the left to the right.

The length of a journey on a string is the number of strings in it. Determine the maximum possible length of a journey on the given string s.