Stack the digits of number

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$0^0$ is defined as $1$ in this question.

1.I have a natural number $N$, $N=\overline{a_1a_2a_3\cdots a_n}$, where $\overline{a_1a_2a_3\cdots a_n}$ denotes the number in decimal representation.

2.If $N$ is smaller than $10$, stop the iteration.

3.I reverse stack the digits into an exponential tower like this:$M=a_{n}^{a_{n-1}^{a_{n-2}^{.^{.^{.^{a_1}}}}}}$.

4.Then I let $N=M$, return to 1.

For example, if the initial $N$ is $26$, the iterative sequence is $26\rightarrow36\rightarrow216\rightarrow6$.

I would like to know that if there are numbers that cannot stop the iteration except for $25$.