How to enhance-iterate by reference over an array element that's of type set (STL) of user-defined objects?

necklace is a c-array consisting of elements that are set<Pearl>, where Pearl is a user-defined type.

necklace is defined as follows

set<Pearl> necklace[NUM_CIRC] = { };

After this the elements are populated with the Pearl's.

The following snippet

for (Pearl &p : necklace[circular_coordinate]) {
    p.set_color("white");
}

results in a compile error

invalid initialization of reference of type 'Pearl&' from expression of type 'const Pearl'

How can I access necklace[circular_coordinate] is a non-const fashion?