Goal
Given a graph of logic gates, can you deduce the values of expected nodes?
In the example case, from (1) a or b -> d and (2) a=0, d=1, we can deduce that b=1.
Based on the other dependency rules, we got c=0, f=0, g=1 and h=1.
So the output for h c g is 101.
Input
line 1: the observations for some of the nodes, formatted as node name:value, separated by a space
line 2: the names of the nodes to output, separated by a space
line 3: number of dependency rules n
following n lines: the dependency rules on the graph. formatted as node_a operation node_b -> node_c, meaning that node_c is the result of the operation on node_a and node_b
Output
a single concatenated string containing the values of the specified nodes in the given order.
Constraints
every node's value is either 1 or 0.
operation: or, and, xor.
node name is alphanumeric and always starts with a letter.
While multiple solutions may exist for a given graph, the sequence of values for the output nodes is guaranteed to be unique.
Example
Input
a:0 d:1 e:0
h c g
5
f or g -> h
d or e -> g
a xor c -> f
b and c -> e
a or b -> d
