Factorial Product

Let \(N = 1!\cdot 2! \cdot 3! \cdot 4! \ldots 9! \cdot 10!\). Let \(2^k\) be the largest power of \(2\) that divides \(N\). What is the value of \(k\)?

Details and assumptions

\(n! = n\times (n-1) \times (n-2) \ldots 2 \times 1\).

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