Binary Sequence Transformation

Given a binary sequence \(a_1, a_2, \ldots, a_n\) of length \(n\), you must perform \(n\) operations sequentially. In the \(i\)-th operation (\(1 \le i \le n\)), perform the following two transformations:

1. Reverse the subarray \([1, i]\): The sequence \(a_1, a_2, \ldots, a_i\) becomes \(a_i, a_{i-1}, \ldots, a_1\).
2. Flip the bits in the subarray \([1, i]\): For every \(1 \le j \le i\), if \(a_j = 0\) it becomes \(1\), and if \(a_j = 1\) it becomes \(0\).

After executing all \(n\) operations, output the final state of the sequence.

inputFormat

The first line contains a single integer \(n\) (\(1 \le n \le 10^5\)), the length of the sequence.

The second line contains \(n\) space-separated integers, each either \(0\) or \(1\), representing the initial sequence \(a_1, a_2, \ldots, a_n\).

outputFormat

Output the final sequence after performing all the operations. Print \(n\) integers separated by a space.

sample

1
0

1