A852.Block Game--Bronze

Farmer John is trying to teach his cows to read by giving them a set of $N$
spelling boards typically used with preschoolers ($1 \leq N \leq 100$). Each
board has a word and an image on each side. For example, one side might have
the word 'cat' along with a picture of a cat, and the other side might have
the word 'dog' along with a picture of a dog. When the boards are lying on the
ground, $N$ words are therefore shown. By flipping over some of the boards, a
different set of $N$ words can be exposed.
To help the cows with their spelling, Farmer John wants to fashion a number of
wooden blocks, each embossed with a single letter of the alphabet. He wants to
make sufficiently many blocks of each letter so that no matter which set of
$N$ words is exposed on the upward-facing boards, the cows will be able to
spell all of these words using the blocks. For example, if $N=3$ and the words
'box', 'cat', and 'car' were facing upward, the cows would need at least one
'b' block, one 'o' block, one 'x' block, two 'c' blocks, two 'a' blocks, one
't' block, and one 'r' block.
Please help the Farmer John determine the minimum number of blocks for each
letter of the alphabet that he needs to provide, so that irrespective of which
face of each board is showing, the cows can spell all $N$ visible words.

Line 1 contains the integer $N$.
The next $N$ lines each contain 2 words separated by a space, giving the two
words on opposite sides of a board. Each word is a string of at most 10
lowercase letters.

Please output 26 lines. The first output line should contain a number
specifying the number of copies of 'a' blocks needed. The next line should
specify the number of 'b' blocks needed, and so on.

In this example, there are $N = 3$ boards, giving $2^3 = 8$ possibilities for
the set of upward-facing words:
fox dog car
fox dog bus
fox cat car
fox cat bus
box dog car
box dog bus
box cat car
box cat bus
We need enough blocks for each letter of the alphabet so that we can spell all
three words, irrespective of which of these eight scenarios occurs.