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For  n = 3, n = 4, input_1 is UNSOLVABLE while rest are SOLVABLE. For n = 5, all are SOLVABLE (come up with an UNSOLVABLE one and test - it must work also)

h1: misplacement
h2: manhattan 
h3: euclidean + floor

Long-time cases
h1: n=4, input 2, 3, 4
h2: 
h3: n=4, input 2, 4

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