Towers of Powers of 17

1717171717\huge\color{#E81990}{17}^{\color{#D61F06}{17}^{\color{#3D99F6}{17}^{\color{#20A900}{17}^{\color{#EC7300}{17}}}}}

Determine the last two digits of the number above.


CS solutions as well as NT solutions will be appreciated.
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