Point coloration refers to animal coat coloration with a pale body and relatively darker extremities: face, ears, feet, tail, and (in males) scrotum. Colorpointed breeds occurs in certain species of rabbits, rats, sheep and horses, but most are found in the family of cats (Felidae) where it is a form of partial albinism resulting from a mutation in tyrosinase — an enzyme involved with melanin production. The mutated enzyme is thermolabile: it fails to work at normal body temperatures, but becomes active in cooler areas of the skin. As a result, dark pigment is limited to the coldest areas of the body, that is, the extremities. Pointed kittens are born white, since the womb is uniformly warm. As the kittens age, the cooler areas darken while warmer areas remain cream to white in color.

An example of a colorpointed cat is the Birman (also called the "Sacred Cat of Burma"), a domestic long-haired breed that is distinguished by a silky coat, deep blue eyes and contrasting white "gloves" or "socks" on each paw. The breed name is derived from Birmanie, the French name for Burma. Recognized point colors are seal, chocolate, blue and lilac (a softer silver-grey).

When breeding Birman pure-lines, it is essential to have some basic understanding of the genetics that determines what point colors the litter of a couple of cats may have. Each cat has two C-genes $$c_p$$ and $$c_m$$ where the first is paternal and the second is maternal in ancestry. In addition, each cat also has two D-genes $$c_p$$ and $$c_m$$ where again the first is paternal and the second is maternal in ancestry. The point color is completely determined by the combination of these four genes.

There are two alleles (alternative forms) of the C-gene that we will represent by the letters C and c, and two alleles of the D-genes that we will represent by the letters D and d. As a result, we can represent the cat's point coloration genotype by the string $$c_pc_md_pd_m$$, with $$c_p, c_m \in \{\texttt{C}, \texttt{c}\}$$ and $$d_p, d_m \in \{\texttt{D}, \texttt{d}\}$$. The relationship between the 16 possible genotypes of the C-genes and D-genes and the resulting point colors is given in the following color table, where we have used the abbreviation choc for the point color chocolate.

A Birman having genotype $$c_pc_md_pd_m$$ randomly passes one of its two C-genes ($$c_p$$ or $$c_m$$) and one of its two D-genes ($$d_p$$ or $$d_m$$) on to each of its kittens. In other words, the cat passes one of four possible combinations $$gh$$ of a C-gene $$g$$ and a D-gene $$h$$ on to each of its kittens, with $$g \in \{c_p, c_m\}$$ and $$h \in \{d_p, d_m\}$$. It is custom practice to fix a generic order of these four possible combinations in the following way: $$c_pd_p$$, $$c_pd_m$$, $$c_md_p$$ and $$c_md_m$$.

If a male Birman with genotype $$c_pc_md_pd_m$$ mates with a female Birman with genotype $$c'_pc'_md'_pd'_m$$, each of their kittens has a genotype $$gg'hh'$$, where $$g \in \{c_p, c_m\}$$, $$g' \in \{c'_p, c'_m\}$$, $$h \in \{d_p, d_m\}$$ and $$h' \in \{d'_p, d'_m\}$$. Because the C-genes and D-genes are independently passed on to the offspring, each possible genotype of the kittens occurs with equal chance.

Geneticist Reginald Punnet invented a diagram that visually represents the possible genotypes of a particular crossing of two cats: the Punnett square. This is a $$4 \times 4$$ grid whose rows are labeled top to bottom with the four possible combinations of the genes that are passed on by the male cat (in their generic order). The columns are labeled left to right with the four possible combinations of the genes that are passed on by the female cat (again in their generic order). Each cell of the grid then contains the genotype of a kitten resulting from the combination of the paternal and maternal genes.

By determining the corresponding point color for each possible genotype of the kittens, breeders use the Punnett square to derive the distribution of point colors in the offspring of the crossed cats. This is an example of a Punnett square for a male and female Birman that both have genotype CcDd.

From this diagram we can derive that the first generation of kittens will have a distribution 9:3:3:1 of the point colors seal:chocolate:blue:lilac.

Assignment

We represent the genotype of a Birman by a string $$c_pc_md_pd_m$$ (str) of four letters, where $$c_p, c_m \in \{\texttt{C}, \texttt{c}\}$$ and $$d_p, d_m \in \{\texttt{D}, \texttt{d}\}$$. Your task:

• Write a function color that takes the genotype (str) of a Birman. The function must return the point color (str) of the Birman: seal, chocolate, blue or lilac.

• Write a function combinations that takes the genotype (str) of a Birman. The function must return the four possible combinations of C-genes and D-genes that the Birman may pass on to its offspring, listed in the generic order. This result must be represented as a list of 2-letter strings (str).

• Write a function punnett that takes the genotypes (str) of a male and a female Birman. The function also has an optional third parameter pprint that takes a Boolean value (bool, default value: False). The function must return the Punnett square that contains the possible genotypes of the first generation kittens of the two cats whose genotypes are given. If the value False was passed to the parameter pprint, the result must be returned as a list of lists (list), where the inner lists represent the successive rows of the square. If the value True was passed to the parameter pprint, the result must be returned as a string (str), where the rows of the square are at separate lines and the genotypes on the same row are separated from each other by a single space.

• Write a function color_distribution that takes the genotypes (str) of a male and a female Birman. The function must return a dictionary (dict) whose keys are the point colors (str) that may occur in the offspring of the two cats whose genotypes are given: seal, chocolate, blue and/or lilac. For each color that is used as a key in the dictionary, the associated value (int) must indicate how many of the 16 possible genotypes of the kittens result in that particular color.

Example

>>> color('CcDd')
'seal'
>>> color('ccdd')
'lilac'

>>> combinations('CcDd')
['CD', 'Cd', 'cD', 'cd']
>>> combinations('ccdd')
['cd', 'cd', 'cd', 'cd']

>>> punnett('CcDd', 'CcDd')
[['CCDD', 'CCDd', 'CcDD', 'CcDd'], ['CCdD', 'CCdd', 'CcdD', 'Ccdd'], ['cCDD', 'cCDd', 'ccDD', 'ccDd'], ['cCdD', 'cCdd', 'ccdD', 'ccdd']]
>>> print(punnett('CcDd', 'CcDd', pprint=True))
CCDD CCDd CcDD CcDd
CCdD CCdd CcdD Ccdd
cCDD cCDd ccDD ccDd
cCdD cCdd ccdD ccdd
>>> print(punnett('cCDd', 'CcdD', pprint=True))
cCDd cCDD ccDd ccDD
cCdd cCdD ccdd ccdD
CCDd CCDD CcDd CcDD
CCdd CCdD Ccdd CcdD

>>> color_distribution('CcDd', 'CcDd')
{'blue': 3, 'seal': 9, 'lilac': 1, 'chocolate': 3}
>>> color_distribution('cCDD', 'cCDD')
{'seal': 12, 'chocolate': 4}
>>> color_distribution('ccDD', 'ccDD')
{'chocolate': 16}
>>> color_distribution('ccdd', 'CcDd')
{'blue': 4, 'lilac': 4, 'seal': 4, 'chocolate': 4}