Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Antichain

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have a directed acyclic graph *G*, consisting of *n* vertexes, numbered from 0 to *n* - 1. The graph contains *n* edges numbered from 0 to *n* - 1. An edge with number *i* connects vertexes *i* and (*i* + 1) *mod* *n*, and it can be directed in either direction (from *i* to (*i* + 1) *mod* *n*, or vise versa).

Operation *x* *mod* *y* means taking the remainder after dividing number *x* by number *y*.

Let's call two vertexes *u* and *v* in graph *G* comparable if the graph contains a path either from *u* to *v* or from *v* to *u*. We'll assume that an antichain is a set of vertexes of graph *G*, where any two distinct vertexes are not comparable. The size of an antichain is the number of vertexes in the corresponding set. An antichain is maximum if the graph doesn't have antichains of a larger size.

Your task is to find the size of the maximum antichain in graph *G*.

Input

The first line contains the sequence of characters *s*_{0}*s*_{1}... *s*_{n - 1} (2 ≤ *n* ≤ 10^{6}), consisting of numbers zero and one. The length of the line (number *n*) corresponds to the number of vertexes and edges in graph *G*. If character *s*_{i} (*i* ≥ 0) equals 0, then the edge between vertexes *i* and (*i* + 1) *mod* *n* is directed from the *i*-th vertex to the (*i* + 1) *mod* *n*-th one, otherwise — to the opposite point.

It is guaranteed that the given graph is acyclic.

Output

Print a single integer — the size of the maximum antichain of graph *G*.

Examples

Input

001

Output

1

Input

110010

Output

3

Note

Consider the first test sample. The graph's *G* edges are: 0 → 1, 1 → 2, 0 → 2. We can choose the set of vertexes [0] as the maximum antichain. We cannot choose an antichain of larger size.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/18/2019 13:23:05 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|