--description--

For non-negative integers $m$, $n$, the Ackermann function $A(m, n)$ is defined as follows:

$$A(m, n) = \begin{cases} n + 1 & \text{if $m = 0$} \\ A(m - 1, 1) & \text{if $m > 0$ and $n = 0$} \\ A(m - 1, A(m, n - 1)) & \text{if $m > 0$ and $n > 0$} \end{cases}$$

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 ${14}^8$.

--hints--

ackermanFunction() should return 1098988351.

assert.strictEqual(ackermanFunction(), 1098988351);

--seed--

--seed-contents--

function ackermanFunction() {

  return true;
}

ackermanFunction();

--solutions--

// solution required