Small W will take part in CET-6 test which will be held on December $20^{th}$. In order to pass it he must remember a lot of words.
He remembers the words according to Ebbinghaus memory curve method.
He separates the words into many lists. Every day he picks up a new list, and in the next $1^{st}, 2^{nd}, 4^{th}, 7^{th}, 15^{th}$ day, he reviews this list.
So every day he has many lists to review. However he is so busy, he does not know which list should be reviewed in a certain day. Now he invites you to write a program to tell him which list should to be reviewed in a certain day.
Lists are numbered from 1. For example list 1 should be reviewed in the $2^{nd}, 3^{rd}, 5^{th}, 8^{th}, 16^{th}$ day.
Multi test cases (about 100), every case contains an integer n in a single line.
Please process to the end of file.
[Technical Specification]
$2 \leq n \leq 100000$
For each n，output the list which should be reviewed in the $n^{th}$ day in ascending order.