How do describe the composition of an indicator function?

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I have an indicator function:

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I have to describe the composition in this form:

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I replaced the 'n' value with the function but I cannot simplify it, how can one describe and simplify the composition of an indicator function?

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Hint: Calculate $f(f(n))$ for $0\le n\le4$, for $n=5, 6$, and for $n>6$.