Mod and Factorial

Let’s define the function f(N) = n which removes all trailing zeros from N to get n, where n and N are integer numbers. For example: f(12345) = 12345, f(678000) = 678, f(4560007) = 4560007, f(10000000) = 1 and so on. Now, can you find :
f(100!) mod 100?

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