CF1895D.XOR Construction

普及/提高-

通过率：0%

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You are given $n-1$ integers $a_1, a_2, \dots, a_{n-1}$ .

Your task is to construct an array $b_1, b_2, \dots, b_n$ such that:

every integer from $0$ to $n-1$ appears in $b$ exactly once;
for every $i$ from $1$ to $n-1$ , $b_i \oplus b_{i+1} = a_i$ (where $\oplus$ denotes the bitwise XOR operator).

The first line contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ).

The second line contains $n-1$ integers $a_1, a_2, \dots, a_{n-1}$ ( $0 \le a_i \le 2n$ ).

Additional constraint on the input: it's always possible to construct at least one valid array $b$ from the given sequence $a$ .

Print $n$ integers $b_1, b_2, \dots, b_n$ . If there are multiple such arrays, you may print any of them.