## Problem B: Octagons

Below is a picture of an infinite hyperbolic tessellation of octagons.
If we think of this as a graph of vertices (of degree three), then
there exists an isomorphism of the graph which maps any vertex *x*
onto any other vertex *y*. Every edge is given a label from the set
*{a,b,c}* in such a way that every vertex has all three types of
edges incident on it, and the labels alternate around each octagon.
Part of this labeling is illustrated in the diagram.

So a path in this graph (starting from any vertex) can be specified by
a sequence of edge labels. Your job is to write a program which, given
a squence of labels such as "abcbcbcabcaccabb", returns "closed" if
the path ends on the same vertex where it starts, and returns
"open" otherwise.

### Input Specification

The input will begin with a number *Z* ≤ 200 on a line by itself. This is followed
by *Z* lines, each of which is a squence of length at least 1 and at most 40
of 'a's 'b's and 'c's.
### Sample Input

2
abababab
abcbcbcbcba

### Output Specification

For each input instance, the output will be the words
"closed" or "open", each on a single line.
### Output for Sample Input

closed
open

*Danny Sleator*