You have beads of several different colors that are to be placed on a string, with the requirement that for any group of three adjacent beads, all three must have different colors.
You are given a int beads indicating how many of each color bead you have. The i-th element of beads is the number of beads of color i, where each i represents a distinct color. You are to return a long representing the number of ways they can be placed on the string, meeting the given requirement.
|-||The resulting arrangement of beads is linear, not circular. (Thus, the first bead on the string, and the last, are not adjacent.)|
|-||beads will contain between 3 and 5 elements, inclusive.|
|-||Each element of beads will be between 1 and 10, inclusive.|
|-||The total number of beads will not exceed 35.|