Holes in Numbers

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Have you ever noticed that \(0\), \(6\), \(8\) and \(9\) have holes in them?

An interesting problem is to count such holes in a given number.

For example, the number \(68724\) and \(59013\) have \(3\) and \(2\) holes respectively.

Counting the holes in relatively small numbers are pretty easy, but how about finding the holes in a 500 digits number?

How many holes are there in the 500-digits number?

You can find the number here.


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