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282. The Ackermann function

For non-negative integers $m$, $n$, the Ackermann function $A(m,n)$ is defined as follows: $$A(m,n)=\{\begin{array}{ll}n+1& \text{ if }m=0\\ A(m-1,1)& \text{ if }m>0\text{ and }n=0\\ A(m-1,A(m,n-1))& \text{ if }m>0\text{ and }n>0\end{array}$$

For example $A(1,0)=2$, $A(2,2)=7$ and $A(3,4)=125$.

Find ${\displaystyle \sum _{n=0}^{6}A(n,n)}$ and give your answer mod ${14}^8$.