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Poveste şi cerinţă...

Seeking treasures of immense value to add to his almighty random knapsack, Prosto is travelling around the world. During one of his journeys he found a room filled with chests, each being locked. On every chest there is a boolean formula engraved on it.
 
The boolean formulas are XOR sums of multiple clauses, where a clause is the AND sum of some literals, which can be negated.
 
Alongside the formula on the chest, there is engraved a number $k$, which represents the number of distinct literals which can appear in the given formula. The $i$-th literal is represented as the $i$-th lowercase letter of the english alphabet e.g. the first literal is 'a', the second literal is 'b' and so on.
 
In order to unlock a chest you need to find the number of ways to assign each literal $0$ or $1$ such that the given formula evaluates to $1$.
 
Let's say we have a chest with $k=3$ variables and the following formula: (a AND b) XOR (b AND c) XOR (a AND c). If the tuple of literals $(a,b,c)$ is equal to one of the following tuples: $(1,1,0)$, $(1,0,1)$, $(0,1,1)$, $(1,1,1)$ then the given expression is $1$, so the answer is $4$.
 
Our protagonist promises you glory and $100$ points if you can help him find the keys to some of his chests.

h2. Date de intrare