There were several small cubes with the multi-colored sides laying around the cylinder which inclosed the Hypercube. It’s highly possible that you need to use them somehow to remove the force field.

Your task is to return the maximum possible height of the tower built from the cubes in such a way that each of four its side sides are of the same color (4 sides - 4 colors, each side has its own color).

Each cube is described by a string of 6 letters in capital Latin characters which represent the color of the respective side (A — Azure, B — Blue, C — Cyan, G — Green, O — Orange, R — Red, S — Scarlet, V — Violet, W — White, Y — Yellow).

The sides are numbered in the following order: front, right, left, back, top, bottom. A cube doesn’t have two sides of the same color.

You may rotate each cube as you wish to build the tower.

**Input: ** Array of the cubes descriptions.

**Output: ** Maximum height of the tower.

**Example:**

tower(['GYVABW', 'AOCGYV', 'CABVGO', 'OVYWGA']) == 3 tower(['ABCGYW', 'CAYRGO', 'OCYWBA', 'ACYVBR', 'GYVABW']) == 1

**How it is used: **
For the geometry analysis.

**Precondition**:

2 <= number of cubes <= 10