The set of tokens of the language is {+,-,^,NUMBER}. The token NUMBER represents unsigned integers, i.e., non-empty sequences of digits. Recall that 1,+2, 3^4^5 and -6^-7 (even strange expressions like --8^+++9, which is equivalent to 8^9), are correct, whereas +, 1+2, 3^, 1 2 are not. The generated AST must correspond to an interpretation of ^ as a right-associative with higher precedence than the unary operators. For example, for input -1^2^+3 the resulting AST must be -(^(1,^(2,+(3)))), i.e., like if the implicit parenthesization was -(1^(2^(+3))).