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In the process of generating a clonal mammalian cell line, a single cell was seeded in a well of a cell culture plate. After the first $48$ hours, one of the progeny cells underwent apoptosis due to a new mutation. If the doubling time of the cells is $24$ hours and no more cell death occurs, the total number of cells after a total of $7$ days from seeding will be $\_\_\_\_$. (answer in integer)

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