Practice Sets and Probability with the exercise "Set Probabilities (Card Game)"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

You have a deck of the card game set and n current cards drawn on the table. Determine the probability that after drawing 1 more card, you can form a set from the current cards.

The deck consists of one copy of each possible combination of 4 unique features with 3 variations each (a total of 81 cards). The features and variations are as follows:
Number: 1, 2, or 3
Shading: OUTLINED, STRIPED, or SOLID
Color: RED, GREEN, or PURPLE
Shape: DIAMOND, OVAL, or SQUIGGLE

For example, a card could be 2 SOLID GREEN OVAL or 1 STRIPED PURPLE SQUIGGLE.

A set is formed with three cards which display each feature either all the same or all different. It is not a set if two cards share a feature but the other card does not. For example, these are all valid sets:

1 STRIPED RED OVAL
2 STRIPED PURPLE OVAL
3 STRIPED GREEN OVAL

2 SOLID PURPLE OVAL
2 SOLID PURPLE DIAMOND
2 SOLID PURPLE SQUIGGLE

1 OUTLINED PURPLE DIAMOND
2 SOLID RED OVAL
3 STRIPED GREEN SQUIGGLE

And these are all invalid sets:

1 SOLID RED OVAL
1 OUTLINED RED OVAL
1 STRIPED GREEN OVAL

3 OUTLINED PURPLE DIAMOND
2 STRIPED PURPLE SQUIGGLE
3 SOLID PURPLE SQUIGGLE

1 SOLID RED DIAMOND
2 STRIPED PURPLE OVAL
2 STRIPED GREEN OVAL

Note that the card you draw does not have to be used in the sets formed if there are already sets on the table.

Input

Line 1: An integer n for the number of cards currently on the table
Next n lines: Four space separated features describing a card in the following order: Number, Shading, Color, Shape.

Output

Line 1: A probability p as a decimal from 0 to 1 rounded to 4 decimal places.

Constraints

2 ≤ n ≤ 20

Example

Input

2
2 SOLID RED SQUIGGLE
1 OUTLINED GREEN SQUIGGLE

Output

0.0127

Solve it

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