You complete me

Logic Level 3

197×1091811000099 19681\large{\begin{array}{lllllllll}&&&&&1&9&7&\square\\\times&&&&&1&0&\square&9\\\hline &&&&1&\square&8&1&1\\&&&&\square&0&0&\square&\\&&&0&\square&\square&0&&&\\&&\square&9&\square&9&&&\\ \hline &\ &1&9&\square&6&8&\square&1\\\hline\end{array}}

Above shows an incomplete long multiplication. What is the maximum number of digits I can still remove to allow only one unique solution?

Details and Assumptions:

  • For example, I can remove one of the number "1" in the very last column and I'm still able to find the unique solution. So I can remove at least more digit to allow one unique solution.

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