Factorial Product

Let N=1!2!3!4!9!10!N = 1!\cdot 2! \cdot 3! \cdot 4! \ldots 9! \cdot 10!. Let 2k2^k be the largest power of 22 that divides NN. What is the value of kk?

Details and assumptions

n!=n×(n1)×(n2)2×1n! = n\times (n-1) \times (n-2) \ldots 2 \times 1.

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