Xor Pyramid Diagonal

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.

Input

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.

Output

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

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le a_i \le 10^9$

Example

Input

8
2 10 5 12 9 5 1 5

Output

2 8 7 1 11 4 15 9