Problem Description

Little W has a $01$ sequence $a_1,a_2,\ldots,a_n$ of length $n$. He will perform $n$ operations on this sequence in order.

In the $i$-th operation ($1\le i\le n$), Little W will perform the following two transformations in order:

1. Reverse the numbers in the interval $[1,i]$ by index. Formally, after this transformation, the sequence $a$ becomes $a_i,a_{i-1},\ldots,a_{1},a_{i+1},a_{i+2},\ldots,a_n$.
2. Flip the numbers in the interval $[1,i]$ by value. Formally, after this transformation, for any $1\le j\le i$, if $a_j=0$ then $a_j$ becomes $1$, otherwise $a_j$ becomes $0$.

Little W wants to know the value of each element in the sequence $a$ after all $n$ operations are finished.

Input Format

Read input from standard input.

The first line contains a positive integer $n$, representing the length of the sequence.

The next line contains $n$ integers, representing the sequence $a_1,a_2,\ldots, a_n$. It is guaranteed that $a_i=0$ or $1$.

Output Format

Write output to standard output.

Output one line with $n$ integers, representing the value of each element in the sequence $a$ after all operations.

3
1 1 1

0 0 1 

8
1 0 1 1 1 0 0 1

0 1 0 1 1 1 1 0 

Hint

[Sample Explanation #1]

The changes of sequence $a$ are shown in the table below:

[Sample Explanation #2]

The changes of sequence $a$ are shown in the table below:

[Sample #3]

See revflip/revflip3.in and revflip/revflip3.ans in the contestant files.

[Sample #4]

See revflip/revflip4.in and revflip/revflip4.ans in the contestant files.

[Constraints]

For all data, it is guaranteed that $1\le n\le 2\times 10^6$, and for any $1\le i\le n$, $a_i=0$ or $1$.

Translated by ChatGPT 5