In the above diagram, you must connect every colored box with every other colored box that has the same color. You do this by drawing a (not necessarily straight) line connecting the two boxes.

What is the minimum number of line intersections over all possible ways to connect the boxes?

**Details and Assumptions**

The connecting lines must not go out of the square board.

There cannot be three or more connecting lines concurrent at one point.

Here is one example of a way to connect the boxes with 12 intersections.

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