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Time limit per test: 0.25 second(s)

Memory limit: 65536 kilobytes

Memory limit: 65536 kilobytes

input: standard

output: standard

output: standard

An equilateral triangle with side

Each unit triangle can be colored with two colors in four different ways (numbered from 1 to 4), shown on picture (b). A colored equilateral triangle with side

You are to find the number of different correct colored equilateral triangles that can be assembled from a given set of unit triangles. You're allowed to rotate unit triangles arbitrarily, however, the position of the big triangle is fixed (i.e., the colorings that are rotations of each other are considered different).

sample input | sample output |

2 0 1 0 3 | 3 |

sample input | sample output |

2 1 1 1 1 | 12 |

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