In maths, we do $a\times b=ab$. But if you do that while there is the **log** function, $\color{#D61F06}{\log (a) \times \log (b) = \log (a\times b)}$ then that will be a big mistake!

But for some pairs of integers $(a,b)$, for which $\log (a)$ and $\log (b)$ are also integers, the above property is true. Find the sum of all $a$ and $b$ in these pairs.

If you get $n$ pairs $(a_1,b_1),(a_2,b_2),\ldots,(a_n,b_n)$, then answer should be reported as $\displaystyle \sum_{k=1}^n \biggl(a_k+b_k \biggr)$

**Details and assumptions**:

Assume we take the log in base 10.

We only consider $a$ and $b$ as integers, and so are $\log(a)$ and $\log(b)$