Description

Input

The first line contains the integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of elements in the set $S$.

The next line contains $n$ distinct integers $S_1, S_2, \ldots, S_n$ ($1 \leq S_i \leq 2 \cdot 10^5$) — the elements in the set $S$.

Output

In the first line print the largest non-negative integer $x$, such that there is a magical permutation of integers from $0$ to $2^x - 1$.

Then print $2^x$ integers describing a magical permutation of integers from $0$ to $2^x - 1$. If there are multiple such magical permutations, print any of them.

3
1 2 3

2
0 1 3 2

2
2 3

2
0 2 1 3

4
1 2 3 4

3
0 1 3 2 6 7 5 4

2
2 4

0
0

1
20

0
0

1
1

1
0 1

Note

In the first example, $0, 1, 3, 2$ is a magical permutation since:

• $0 \oplus 1 = 1 \in S$
• $1 \oplus 3 = 2 \in S$
• $3 \oplus 2 = 1 \in S$

Where $\oplus$ denotes bitwise xor operation.