Logical Expression Equivalence

Two logical expressions are given. For each test case, determine whether the two expressions produce the same result for every assignment of their variables.

The first line contains the number of test cases T.

Each test case is given on one line. The two logical expressions that must be compared are written consecutively with no delimiter, so your program must separate the two expressions from that line.

An expression may contain variables a through z, binary operators |, &, ^, the unary operator ~, and parentheses. All other characters are ignored.

Operator precedence follows the C-language order ~, &, ^, |. Binary operators associate from left to right within the same precedence level.

Each expression contains at most 10 distinct variables and at most 100 operators.

For each test case, let N be the test case number starting from 1.

If the two expressions are logically equivalent, print the following format.

Data set N: Equivalent

If they are logically different, print the following format.

Data set N: Different