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# Pen & paper solution
The input program is composed by 14 repeated iterations with slight variations on 3 particular instructions:
- I4: `div z A` where `A` can be either 1 or 26;
- I5: `add x B` where `B` can be any number;
- I15 `add y C` where `C` can be any number.
Below is the table of the three sets of values for each iteration:
| A | B | C
---+----+-----+----
1 | 1 | 13 | 6
2 | 1 | 11 | 11
3 | 1 | 12 | 5
4 | 1 | 10 | 6
5 | 1 | 14 | 8
6 | 26 | -1 | 14
7 | 1 | 14 | 9
8 | 26 | -16 | 4
9 | 26 | -8 | 7
10 | 1 | 12 | 13
11 | 26 | -16 | 11
12 | 26 | -13 | 11
13 | 26 | -6 | 6
14 | 26 | -6 | 1
Each iteration `i` can be modelled with a function `f_i(z,a,b,c)` where `a`, `b`, `c` are the parameters for the given iteration and `z` is the output from the previous iteration (or 0 otherwise).
Function `f_i` can be defined as follows:
```{#iteration}
f_i(z,1,b,c) = z if (z % 26) == i - a
f_i(z,1,b,c) = 26*z + (i + b) otherwise
f_i(z,26,b,c) = z/26 if (z % 26) == i - a
f_i(z,26,b,c) = 26*(z/26) + (i + b) otherwise
```
**Note:** since we are dealing with integer division we cannot simplify `26*(z/26)` with `z`.
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