Consider a xor pyramid where each number is the xor of lower-left and lower-right numbers. Here is an example pyramid:

Given the bottom row of the pyramid, your task is to find the leftmost number of each row.

The first line has an integer $n$ : the size of the pyramid.

The next line has $n$ integers $a_1,a_2,\dots,a_n$ : the bottom row of the pyramid.

• $1 \le n \le 2 \cdot 10^5$
• $1 \le a_i \le 10^9$

Print $n$ integers: the leftmost numbers of the rows from bottom to top.