Permutation Power

Let σ\sigma be a permutation of {1,2,3,,100}\{1, 2, 3, \ldots, 100\}. Then there exists a smallest positive integer f(σ)f(\sigma) such that σf(σ)=id\sigma^{f(\sigma)} = \text{id}, where id\text{id} is the identity permutation.

What is the largest value of f(σ)f(\sigma) over all σ?\sigma?


Note: σk\sigma^k is σ\sigma applied kk times in succession.

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