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1. Iterated piecewise function value ●○○○○ 10 ptsFor integers $n$, let $f(n) = \begin{cases} n^2 + 1 & \text{if } n \text{ is odd}, \\ n^2 - 3n + 1 & \text{if } n \text{ is even}. \end{cases}$ Find $f(f(f(f(f(f(2))))))$.
2. Evaluating the Ackermann function ●●○○○ 20 ptsDefine a function $A(m, n)$ by $$A(m,n) = \begin{cases} n+1 & \text{if } m = 0, \\ A(m-1, 1) & \text{if } m > 0 \text{ and } n = 0, \\ A(m-1, A(m, n-1)) & \text{if } m > 0 \text{ and } n > 0. \end{cases}$$ Compute $A(2, 1)$.