22s in Divisor Product of 3600036000

Let PnP_n be the product of all positive divisors of a positive integer nn. For example, P1=1P_1 = 1 and P4=1×2×4=8.P_4 = 1 \times 2 \times 4 = 8.

If 2m2^m is the highest integer power of 22 that divides P36000P_{36000}, what is mm?

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