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A positive integer is called balanced if the size of its longest strictly decreasing subsequence (in its decimal expression) is the same as the size of its longest non-strictly increasing subsequence.

For example, the number $77429$ is balanced, because both its longest strictly decreasing subsequence ($742$) and its longest non-strictly increasing subsequence ($779$) have length $3$.

There are $2274$ balanced integers below $10^4$.

Find the total number of balanced integers. Give your answer modulo $10^9+7$.

Solution
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