Solve the the following cryptoarithmetic problem. To solve it you need to find a mapping from letters to digits, so that each letter is mapped to a different digit. Remember that the first digit in each of the numbers cannot be 0.

EAT +

THAT =

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APPLE

Write the constraint equations for the problem (remember to use the carry when doing additions).

Solve the problem using backtracking search with the Minimum Remaining Value heuristics to select the variable and the least-constraining value heuristics (if needed) to chose the value. Show the search tree to solve the problem.