Necklace stones puzzle
CJam, 28 bytes

r__&amp;,a\2*e`0f=_2ew::+]::e&gt;S*


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How it works

r    e# Read a whitespace-separated token from STDIN.
__   e# Push two copies.
&amp;    e# Intersect two of the copies (removes duplicates).
,a   e# Calculate the length and wrap it in an array.
\    e# Swap the array with the input string.
2*   e# Repeat the input string two times.
e`   e# Perform run-length encoding.
0f=  e# Keep only the repetitions.
_2ew e# Copy and push the overlapping slices of length two.
::+  e# Add the integers in the resulting slices.
]    e# Wrap the entire stack in an array.
::e&gt; e# Compute the maximum of each of the three arrays.
S*   e# Join, separating by spaces.