You are given an array \[A = 8 , 3 , 2 , 4 ,5 , 6 , 7 , 1 ,9,10,11,12,13 \] of size \(n\). As long as the array is not sorted, in each step, a subset of \(A\) is randomly permuted. This subset is optimally chosen each time so that \(A\) is sorted in the least amounts of steps. What is the expected value of the total number of times this operation needs to be done in order to sort \(A\)?

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