fixpoint

base64(base64(base64(base64(...))))

Fun fact (September 27): If you take any string, you and base64 encode it repeatedly, you will eventually get to the string Vm0wd2QyUXlVWGxWV0d4V1YwZDRWMVl3WkRSV01WbDNXa1JTVjA..., which I think is fairly neat. But that is for the standard and boring base64 alphabet (ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/).

I said to myself, what if I use a different base64 alphabet? So I made my own base64 alphabet, which is

bctf{?????????????????????????FiXed???????????????????????p01nT}

(In which the question marks are for you to figure out.)

When using my alphabet, base64 encoding any string repeatedly eventually gives you

NslSBwm6YNHHNreCNsmojw8zY9nGVzep9NoJ5LHpH3b8NKnQlB2Ca{XzIxeUyR85Y{COjRD09P4mFEAAFACZlAo0jwnGBrj7UAbwYBHDjBDEjBlMY{DWkE46YrVtaKh6ABDdVLoty{5Gjr5DMrmSNAo05DVu5NjR93m9VEDqMfHcjr5rAr2WVPo0lBVGaxA{N3mvBw8cYzbL5DHLlB8GBxrzYNo95B52N9HCIR4Ol3mcaxm3AocWkE2tArVeF{D0NxlvVrm6UElHFKmklB5CNE2tU{VtFPmp9B8WUNAtlNmUUBefyACwNR7zY9leFEwzj9nxARvDks5caoHo5sv{k{8ZYPH9aKwRABASy{HqY9vSjxAfNrBOVDA0As5EBEL7UBCZALAUj35SNKLAABmoHsocj6VUBxVp9NoSHBHDV64GU98ZjAmR5Evzl9leYweWl3lRFRv0UD4HB{X8IBv6BrDtjAl8Fwe29NoRBR4Zj9HUarmgAr5ck{DzlBAt5B76ABmf9rDkjAAGkzANNrvkjBDtY9nCaRnxMxH9ABmZAsb8NKnNy{mC5DIRl{VAUNeMMrDvBxADVs4SU92o93VoAR7zYDmEBsI7ABjwy{m09femjsIRjsm{VE4cYfeEVRBOUB8WBrmylD4GUBeAI3mvHwDOl9luFw5pY{mcVfAtlzHcjKLKU3m{MR4cjBVuFrDUNsmRMR4t5P5HU98fIAmJF{LZyfocjKLMj3ldU{8qYr88FRLflB5mBK20ArDANKAlN3m{VrmZjB59az5NANrOYzrzAKncBxVp9B5v5BmzyNVcjK46F3vvkfoKH9LGawoyMslvFLHDlElHHKADAomtNLAtUDVtaKL8Y{jw5LAtHBDmkRLRyPV{NR78YPAEVzA793vvILHKj35SFrexMrvkyLBzY3vlBx5xMrm9VBHO5DAUaRLyNACwVfAjlBeAUNeKyBDvyrH0ND48HKnxMrvkN9hzYE5AFze293CZU{Hy...

I challenge you to determine using the above information what is my custom base64 alphabet.