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Sort the following functions in increasing order of magnitude, that is from the smaller to larger growth rate. If two of them are asymptotically of the same order, you should note it. Explain your answer by comparing every two consecutive functions in your sorted order.

22nlog(n!)logn33n6n!log10nlognnenn2nnloglognlog10nn2n!10n(loglognlogn)loglognlognnlogn(n4)