Order the given functions by increasing growth rate.

$f_1(n)=3^n$

$f_2(n)=nlo{g}_{2}n$

$f_3(n)=lo{g}_{4}n$

$f_4(n)=n$

$f_5(n)=5^{lo{g}_{2}n}$

$f_6(n)=n^2$

$f_7(n)=\sqrt[\phantom{2}]{n}$

$f_8(n)=2^{2n}$

As an answer, provide a string of length exactly eight $($with no spaces or quotes$)$ containing the indices of eight

functions $($so$,$ the first number indicates the function with the slowest growth rate, while the last number

indicates the function with the highest growth rate$).$ For example, for a similar, but simpler problem $f_1(n)=2^n,$

$f_2(n)=lo{g}_{2}n,f_3(n)=n^2$ the answer would be $231$