Description:
This is an interactive problem.
Ayush devised yet another scheme to set the password of his lock. The lock has $$$n$$$ slots where each slot can hold any non-negative integer. The password $$$P$$$ is a sequence of $$$n$$$ integers, $$$i$$$-th element of which goes into the $$$i$$$-th slot of the lock.
To set the password, Ayush comes up with an array $$$A$$$ of $$$n$$$ integers each in the range $$$[0, 2^{63}-1]$$$. He then sets the $$$i$$$-th element of $$$P$$$ as the bitwise OR of all integers in the array except $$$A_i$$$.
You need to guess the password. To make a query, you can choose a non-empty subset of indices of the array and ask the bitwise OR all elements of the array with index in this subset. You can ask no more than 13 queries.
Input Format:
The first line of input contains one integer $$$n$$$ $$$(2 \le n \le 1000)$$$ — the number of slots in the lock.
Output Format:
None
Note:
The array $$$A$$$ in the example is $$$\{{1, 2, 4\}}$$$. The first element of the password is bitwise OR of $$$A_2$$$ and $$$A_3$$$, the second element is bitwise OR of $$$A_1$$$ and $$$A_3$$$ and the third element is bitwise OR of $$$A_1$$$ and $$$A_2$$$. Hence the password sequence is $$$\{{6, 5, 3\}}$$$.