Determine if a set of equations like "a==b" and "a!=b" over single-letter variables is satisfiable by grouping variables connected by equalities (e.g., with union-find) and checking that no inequality relates variables in the same group. There are at most 26 lowercase variables and up to 500 equations.
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You are given an array of strings equations that represent relationships between variables where each string equations[i] is of length 4 and takes one of two different forms: "xi==yi" or "xi!=yi".Here, xi and yi are lowercase letters (not necessarily different) that represent one-letter variable names. Return true if it is possible to assign integers to variable names so as to satisfy all the given equations, or false otherwise.
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